Difference between revisions of "Geometric"
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https://jira.secondlife.com/browse/WEB-235''' | https://jira.secondlife.com/browse/WEB-235''' | ||
''So that I can expand each function into deeper detail without the page starting to fail in readability.'' --[[User:Nexii Malthus|Nexii Malthus]] 23:05, 24 October 2008 (UTC) | ''So that I can expand each function into deeper detail without the page starting to fail in readability.'' --[[User:Nexii Malthus|Nexii Malthus]] 23:05, 24 October 2008 (UTC) | ||
:Break it up so each major section has its own page... thats why hypertext was invented. -[[User:Overbrain Unplugged|Overbrain Unplugged]] 13:36, 10 October 2010 (UTC) | |||
== Geometric Library == | |||
__Toc__ | __Toc__ | ||
== Geometric Library | === <div style="font-size: 120%;">[[#Geometric Library|Line Functions]]</div> === | ||
<!--############# LINE NEAREST POINT #############--> | <!--############# LINE NEAREST POINT #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Line | ==== Line and Point, Vector ==== | ||
|- | |- | ||
| | | | ||
Calculates the vector from a point to the closest point on a line | Calculates the vector from a point ''''to'''' the closest point on a line | ||
< | <source lang="lsl2"> | ||
vector gLXdV(vector O,vector D,vector A){ | vector gLXdV(vector O,vector D,vector A){ | ||
return (O-A)-((O-A)*D)*D;} | return (O-A)-((O-A)*D)*D;} | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Line | ==== Line and Point, Distance ==== | ||
|- | |- | ||
| | | | ||
Calculates distance of | Calculates distance of line to point, same as measuring magnitude of Line and Point Vector, but faster on it's own | ||
< | <source lang="lsl2"> | ||
float gLXdZ(vector O,vector D,vector A){ | float gLXdZ(vector O,vector D,vector A){ | ||
vector k = ( A - O ) % D; | vector k = ( A - O ) % D; | ||
return llSqrt( k * k );} | return llSqrt( k * k );} | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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|- | |- | ||
| vector D | | vector D | ||
| Direction of Line | | Direction of Line (unit vector) | ||
|- | |- | ||
| vector A | | vector A | ||
Line 90: | Line 91: | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Line Nearest Point, Nearest Point ==== | ==== Line Nearest Point, Nearest Point ==== | ||
|- | |- | ||
| | | | ||
Returns nearest point on line to given point | Returns nearest point on line to given point | ||
< | <source lang="lsl2"> | ||
vector gLXnX(vector O,vector D,vector A){ | vector gLXnX(vector O,vector D,vector A){ | ||
return gLXdV(O,D,A) + A;} | return gLXdV(O,D,A) + A;} | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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| | | | ||
Shortest vector of two lines | Shortest vector of two lines | ||
< | <source lang="lsl2"> | ||
vector gLLdV(vector O1,vector D1,vector O2,vector D2){ | vector gLLdV(vector O1,vector D1,vector O2,vector D2){ | ||
vector A = O2 - O1; vector B = D1 % D2; | vector A = O2 - O1; vector B = D1 % D2; | ||
return B*( (A*B)/(B*B) );} | return B*( (A*B)/(B*B) );} | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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| | | | ||
Returns the distance between two lines | Returns the distance between two lines | ||
< | <source lang="lsl2"> | ||
float gLLdZ(vector O1,vector D1,vector O2,vector D2){ | float gLLdZ(vector O1,vector D1,vector O2,vector D2){ | ||
vector A = D1%D2;float B = llVecMag(A);A = <A.x/B,A.y/B,A.z/B>; | vector A = D1%D2;float B = llVecMag(A);A = <A.x/B,A.y/B,A.z/B>; | ||
return (O2-O1) * A;} | return (O2-O1) * A;} | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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Closest point of two lines | Closest point of two lines | ||
< | <source lang="lsl2"> | ||
vector gLLnX(vector O1,vector D1,vector O2,vector D2){ | vector gLLnX(vector O1,vector D1,vector O2,vector D2){ | ||
vector nO1 = < O1*D1, O1*D2, 0>; | vector nO1 = < O1*D1, O1*D2, 0>; | ||
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return O1 + D1*t;} | return O1 + D1*t;} | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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| | | | ||
Computes intersection point of two lines, if there is any, else <-1,-1,-1> if none. | Computes intersection point of two lines, if there is any, else <-1,-1,-1> if none. | ||
< | <source lang="lsl2"> | ||
vector gLLxX( vector A, vector B, vector C, vector D ){ | vector gLLxX( vector A, vector B, vector C, vector D ){ | ||
vector | vector b = B-A; vector d = D-C; | ||
float dotperp = b.x*d.y - b.y*d.x; | |||
if (dotperp == 0) return <-1,-1,-1>; | |||
float | vector c = C-A; | ||
float t = (c.x*d.y - c.y*d.x) / dotperp; | |||
return <A.x + t*b.x, A.y + t*b.y, 0>;} | |||
</source> | |||
t = | |||
return <A.x + t* | |||
</ | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Line and Line, two nearest points of lines ==== | ==== Line and Line, two nearest points of lines ==== | ||
|- | |- | ||
| | | | ||
Two closest points of two lines on each line | Two closest points of two lines on each line | ||
< | <source lang="lsl2"> | ||
vector X1;vector X2; | vector X1;vector X2; | ||
gLLnnXX(vector O1,vector D1,vector O2,vector D2){ | gLLnnXX(vector O1,vector D1,vector O2,vector D2){ | ||
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X1 = O1 + D1*t; | X1 = O1 + D1*t; | ||
X2 = X1 + nD1%nD2;} | X2 = X1 + nD1%nD2;} | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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|} | |} | ||
<!--############# LINE AND LINE, | <!--############# LINE AND LINE, NEAREST LINE #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Line and Line, | |||
==== Line and Line, nearest line ==== | |||
|- | |- | ||
| | | | ||
Input two lines, the function will return a list containing two vectors responding to the line nearest between them. As well as two floats corresponding to the scalar value on the two line of where the line has an end located at. | |||
< | <source lang="lsl2"> | ||
list gLLnL( vector v0, vector v1, vector v2, vector v3 ) { | |||
float Eps = 0.000001; vector vx; vector vy; vector va; vector vb; vector vc; | |||
vector | float x; float y; float d0; float d1; float d2; float d3; float d4; | ||
va = v0-v2; vb = v3-v2; if(llVecMag(vb)<Eps) return []; | |||
vc = v1-v0; if(llVecMag(vc)<Eps) return []; | |||
d0 = va*vb; d1 = vb*vc; d2 = va*vc; d3 = vb*vb; d4 = vc*vc; | |||
float den = d4*d3-d1*d1; if( llFabs(den) < Eps ) return []; | |||
float | float num = d0*d1-d2*d3; x = num/den; y = (d0+d1*x)/d3; | ||
vx = v0+vc*x; vy = v2+vb*y; return [vx,vy,x,y]; } | |||
</source> | |||
</ | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| vector | | vector v0 | ||
| | | Point on Line 1 | ||
|- | |||
| vector v1 | |||
| Point on Line 1 | |||
|- | |- | ||
| vector | | vector v2 | ||
| | | Point on Line 2 | ||
|- | |- | ||
| vector | | vector v3 | ||
| | | Point on Line 2 | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| | | [vx] | ||
| | | Nearest point on Line 1 to Line 2 | ||
|- | |- | ||
| | | [vy] | ||
| | | Nearest point on Line 2 to Line 1 | ||
|- | |- | ||
| | | [x] | ||
| | | Scalar value representing location of vx on line 1 (range [v0,v1]) | ||
|- | |- | ||
| [y] | |||
| Scalar value representing location of vy on line 2 (range [v2,v3]) | |||
| | |||
| | |||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
''' | '''3D'''</div> | ||
<div style="float:right;font-size: 80%;"> | <div style="float:right;font-size: 80%;"> | ||
By Nexii Malthus</div> | By Nexii Malthus</div> | ||
|} | |} | ||
<!--############# | <!--############# LINE AND LINE SEGMENTS, NEAREST LINE #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Line and | |||
==== Line and Line Segments, nearest line segment ==== | |||
|- | |- | ||
| | | | ||
Input two line segments, the function will return a list containing two vectors responding to the line segment nearest between them. As well as two floats corresponding to the scalar value on the two line segments of where the line segment has an end located at. | |||
< | <source lang="lsl2"> | ||
list gLSLSnLS( vector v0, vector v1, vector v2, vector v3 ) { | |||
return ( | float Eps = 0.000001; vector vx; vector vy; vector va; vector vb; vector vc; | ||
} | float x; float y; float d0; float d1; float d2; float d3; float d4; | ||
</ | va = v0-v2; vb = v3-v2; if(llVecMag(vb)<Eps) return []; | ||
vc = v1-v0; if(llVecMag(vc)<Eps) return []; | |||
if( llFabs(vc.x + vc.y + vc.z) < Eps ) return []; | |||
d0 = va*vb; d1 = vb*vc; d2 = va*vc; d3 = vb*vb; d4 = vc*vc; | |||
float den = d4*d3-d1*d1; if( llFabs(den) < Eps ) return []; | |||
float num = d0*d1-d2*d3; x = num/den; y = (d0+d1*x)/d3; | |||
if(x<0)x=0; else if(x>1)x=1; if(y<0)y=0; else if(y>1)y=1; | |||
vx = v0+vc*x; vy = v2+vb*y; return [vx,vy,x,y]; } | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| vector | | vector v0 | ||
| Start | | Start of Line Segment 1 | ||
|- | |||
| vector v1 | |||
| End of Line Segment 1 | |||
|- | |||
| vector v2 | |||
| Start of Line Segment 2 | |||
|- | |- | ||
| vector | | vector v3 | ||
| | | End of Line Segment 2 | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| | | [vx] | ||
| | | Nearest point on Line Segment 1 to Line Segment 2 | ||
|- | |||
| [vy] | |||
| Nearest point on Line Segment 2 to Line Segment 1 | |||
|- | |||
| [x] | |||
| Scalar value representing location of vx on Line Segment 1 (range [v0,v1]) | |||
|- | |||
| [y] | |||
| Scalar value representing location of vy on Line Segment 2 (range [v2,v3]) | |||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
''' | '''3D'''</div> | ||
<div style="float:right;font-size: 80%;"> | <div style="float:right;font-size: 80%;"> | ||
By Nexii Malthus</div> | |||
|} | |} | ||
<!--############# LINE AND LINE, TWO NEAREST POINTS, VECTOR AND DISTANCE #############--> | |||
<!--############# | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== | |||
==== Line and Line, two nearest points with vector and distance ==== | |||
|- | |- | ||
| | | | ||
Computes two closest points of two lines, vector and distance | |||
< | <source lang="lsl2"> | ||
float | vector X1;vector X2;vector V1;float Z1; | ||
gLLnnXXVZ(vector O1,vector D1,vector O2,vector D2){ | |||
</ | vector nO1 = < O1*D1, O1*D2, 0>; | ||
vector nO2 = < O2*D1, O2*D2, 0>; | |||
vector nD1 = < D1*D1, O1*D2, 0>; | |||
vector nD2 = < O2*D1, O2*D2, 0>; | |||
float t = ( nD2.x*nD1.y - nD1.x*nD2.y ); | |||
t = ( nD2.y*(nO1.x-nO2.x) - nD2.x*(nO1.y-nO2.y) ) / t; | |||
X1 = O1 + D1*t; | |||
X2 = X1 + CP(nD1,nD2); | |||
V1 = nD1%nD2; | |||
Z1 = llVecMag(V1);} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| vector | | vector O1 | ||
| | | Origin of Line 1 | ||
|- | |- | ||
| | | vector D1 | ||
| | | Direction of Line 1 | ||
|- | |||
| vector O2 | |||
| Origin of Line 2 | |||
|- | |- | ||
| vector | | vector D2 | ||
| | | Direction of Line 2 | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| | | vector X1 | ||
| | | Closest point on line 1 to line 2 | ||
|- | |- | ||
| | | vector X2 | ||
| Closest point on line 2 to line 1 | |||
|- | |||
vector | | vector V1 | ||
| Direction vector of line 1 to line 2 | |||
|- | |||
| float Z1 | |||
| Numerical distance of line 1 to line 2 | |||
|- | |- | ||
| | !style="background-color: #eed0d0" colspan="2"| Requirement | ||
|- | |- | ||
| | |style="background-color: #eed0d0" colspan="2"| global vector X1 | ||
| | |||
|- | |- | ||
| vector | |style="background-color: #eed0d0" colspan="2"| global vector X2 | ||
|- | |- | ||
|style="background-color: #eed0d0" colspan="2"| global vector V1 | |||
|- | |- | ||
| | |style="background-color: #eed0d0" colspan="2"| global float Z1 | ||
| | |||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
''' | '''2D'''</div> | ||
<div style="float:right;font-size: 80%;"> | <div style="float:right;font-size: 80%;"> | ||
By Nexii Malthus</div> | By Nexii Malthus</div> | ||
|} | |} | ||
<!--############# | <!--############# Line and Point, Direction #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== | ==== Line and Point, Direction ==== | ||
|- | |- | ||
| | | | ||
Works out where point (X) is relative to the line of the segment (L0, L1). | |||
< | <source lang="lsl2"> | ||
float gLSPdir( vector L0, vector L1, vector X ){ | |||
return | return (L1.x - L0.x)*(X.y - L0.y) - (X.x - L0.x)*(L1.y - L0.y); | ||
</ | } | ||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
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!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| vector | | vector L0, vector L1 | ||
| | | Start and End of line segment | ||
|- | |- | ||
| vector X | |||
| vector | |||
| Origin of Point | | Origin of Point | ||
|- | |- | ||
Line 582: | Line 583: | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| | | float isLeft( vector L0, vector L1, vector X ) | ||
| Returns | | Returns float, >0 is Left, 0 on Line, <0 is Right, according to line angle | ||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
''' | '''2D'''</div> | ||
<div style="float:right;font-size: 80%;"> | <div style="float:right;font-size: 80%;"> | ||
By Nexii Malthus</div> | Copyright 2001, softSurfer (www.softsurfer.com) (Must accept License #2), LSL-Port By Nexii Malthus</div> | ||
|} | |} | ||
<!--############# PLANE AND | === <div style="font-size: 120%;">[[#Geometric Library|Plane Functions]]</div> === | ||
<!--############# PLANE AND POINT, DISTANCE #############--> | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Plane and | ==== Plane and Point, Distance ==== | ||
|- | |- | ||
| | | | ||
Finds distance | Finds distance of a point from a plane | ||
< | <source lang="lsl2"> | ||
float | float gPXdZ(vector Pn,float Pd,vector A){ | ||
return | return A * Pn + Pd;} | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
Line 608: | Line 611: | ||
|- | |- | ||
| vector Pn | | vector Pn | ||
| Normal of Plane | | Normal of Plane (unit vector) | ||
|- | |- | ||
| float Pd | | float Pd | ||
| Distance of Plane | | Distance of Plane | ||
|- | |- | ||
| vector | | vector A | ||
| Origin of | | Origin of Point | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| return float | | return float gPXdZ | ||
| Returns | | Returns Distance between plane and point | ||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
Line 631: | Line 631: | ||
|} | |} | ||
<!--############# PLANE AND | <!--############# PLANE AND POINT, VECTOR #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Plane and | ==== Plane and Point, Vector ==== | ||
|- | |- | ||
| | | | ||
Finds | Finds vector that points from point to nearest on plane | ||
< | <source lang="lsl2"> | ||
vector | vector gPXdV(vector Pn,float Pd,vector A){ | ||
return | return -(Pn * A + Pd)*Pn;} | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
Line 648: | Line 648: | ||
|- | |- | ||
| vector Pn | | vector Pn | ||
| Normal of Plane | | Normal of Plane (unit vector) | ||
|- | |- | ||
| float Pd | | float Pd | ||
| Distance of Plane | | Distance of Plane | ||
|- | |- | ||
| vector | | vector A | ||
| Origin of | | Origin of Point | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| return vector | | return vector gPXdV | ||
| Returns vector | | Returns vector from point to closest point on plane | ||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
Line 675: | Line 668: | ||
|} | |} | ||
<!--############# PLANE AND | <!--############# PLANE AND POINT, NEAREST POINT #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Plane and | ==== Plane and Point, Nearest point ==== | ||
|- | |- | ||
| | | | ||
Finds | Finds closest point on plane given point | ||
< | <source lang="lsl2"> | ||
vector | vector gPXnX(vector Pn,float Pd,vector A){ | ||
return | return A - (Pn * A + Pd) * Pn;} | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
Line 692: | Line 685: | ||
|- | |- | ||
| vector Pn | | vector Pn | ||
| Normal of Plane | | Normal of Plane (unit vector) | ||
|- | |- | ||
| float Pd | | float Pd | ||
| Distance of Plane | | Distance of Plane | ||
|- | |- | ||
| vector | | vector A | ||
| Origin of | | Origin of Point | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| return vector | | return vector gPXnX | ||
| Returns vector point of | | Returns vector of a point from closest of point to plane | ||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
Line 719: | Line 705: | ||
|} | |} | ||
<!--############# PLANE AND | <!--############# PLANE AND RAY, INTERSECTION DISTANCE #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Plane and | ==== Plane and Ray, Intersection Distance ==== | ||
|- | |- | ||
| | | | ||
Finds | Finds distance to intersection of plane along ray | ||
< | <source lang="lsl2"> | ||
float gPRxZ(vector Pn,float Pd,vector O,vector D){ | |||
return | return -((Pn*O+Pd)/(Pn*D));} | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
Line 736: | Line 722: | ||
|- | |- | ||
| vector Pn | | vector Pn | ||
| Normal of Plane | | Normal of Plane (unit vector) | ||
|- | |- | ||
| float Pd | | float Pd | ||
Line 742: | Line 728: | ||
|- | |- | ||
| vector O | | vector O | ||
| Origin of | | Origin of Ray | ||
|- | |- | ||
| vector D | | vector D | ||
| Direction of | | Direction of Ray | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| return | | return float gPRxZ | ||
| Returns | | Returns float distance of intersection between ray and plane | ||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
Line 759: | Line 745: | ||
|} | |} | ||
<!--############# PLANE AND | <!--############# PLANE AND RAY, VECTOR #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Plane and | ==== Plane and Ray, Vector ==== | ||
|- | |- | ||
| | | | ||
Finds | Finds distance vector along a ray to a plane | ||
< | <source lang="lsl2"> | ||
vector | vector gPRdV(vector Pn,float Pd,vector O,vector D){ | ||
return D * gPRxZ(Pn,Pd,O,D);} | |||
</source> | |||
</ | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
Line 781: | Line 762: | ||
|- | |- | ||
| vector Pn | | vector Pn | ||
| Normal of Plane | | Normal of Plane (unit vector) | ||
|- | |- | ||
| float Pd | | float Pd | ||
| Distance of Plane | | Distance of Plane | ||
|- | |- | ||
| vector | | vector O | ||
| Origin of | | Origin of Ray | ||
|- | |- | ||
| | | vector D | ||
| | | Direction of Ray | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| vector | | return vector gPRdV | ||
| Returns vector along a ray to a plane | |||
| vector | |||
|- | |- | ||
!style="background-color: #eed0d0" colspan="2"| Requirement | !style="background-color: #eed0d0" colspan="2"| Requirement | ||
|- | |- | ||
|style="background-color: #eed0d0" colspan="2"| | |style="background-color: #eed0d0" colspan="2"| function float gPRxZ(vector Pn,float Pd,vector O,vector D) | ||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
Line 813: | Line 789: | ||
|} | |} | ||
<!--############# PLANE AND RAY, | <!--############# PLANE AND RAY, INTERSECTION POINT #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Plane and Ray, | ==== Plane and Ray, Intersection Point ==== | ||
|- | |- | ||
| | | | ||
Finds intersection point along a ray to a plane | |||
< | <source lang="lsl2"> | ||
vector | vector gPRxX(vector Pn,float Pd,vector O,vector D){ | ||
return O + gPRdV(Pn,Pd,O,D);} | |||
</source> | |||
</ | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
Line 834: | Line 806: | ||
|- | |- | ||
| vector Pn | | vector Pn | ||
| Normal of Plane | | Normal of Plane (unit vector) | ||
|- | |- | ||
| float Pd | | float Pd | ||
Line 848: | Line 820: | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| vector | | return vector gPRxX | ||
| Returns vector point of intersection between ray and plane | |||
| vector | |||
|- | |- | ||
!style="background-color: #eed0d0" colspan="2"| Requirement | !style="background-color: #eed0d0" colspan="2"| Requirement | ||
|- | |- | ||
|style="background-color: #eed0d0" colspan="2"| | |style="background-color: #eed0d0" colspan="2"| function vector gPRdV(vector Pn,float Pd,vector O,vector D) | ||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
Line 866: | Line 833: | ||
|} | |} | ||
<!--############# PLANE AND LINE, INTERSECTION POINT #############--> | |||
<!--############# | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== | ==== Plane and Line, Intersection Point ==== | ||
|- | |- | ||
| | | | ||
Finds | Finds interesection point of a line and a plane | ||
< | <source lang="lsl2"> | ||
vector | vector gPLxX(vector Pn,float Pd,vector O,vector D){ | ||
return O + D*-( (Pn*O-Pd)/(Pn*D) );} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| vector Pn | |||
| Normal of Plane (unit vector) | |||
|- | |||
| float Pd | |||
| Distance of Plane | |||
|- | |||
| vector O | |||
| Origin of Line | |||
|- | |||
| vector D | |||
| Direction of Line | |||
|- | |||
!style="background-color: #d0d0ee" | Output | |||
} | |||
</ | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| vector | | return vector gPLxX | ||
| Returns vector point of intersection between line and plane | |||
| vector | |||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
Line 944: | Line 873: | ||
|} | |} | ||
<!--############# | <!--############# PLANE AND PLANE, INTERSECTION LINE #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== | ==== Plane and Plane, Intersection Line ==== | ||
|- | |- | ||
| | | | ||
Finds | Finds line of intersection of two planes | ||
< | <source lang="lsl2"> | ||
vector oO;vector oD; | |||
gPPxL(vector Pn,float Pd,vector Qn,float Qd){ | |||
oD = (Pn%Qn)/llVecMag(Pn%Qn); | |||
vector Cross = (Pn%Qn)%Pn; | |||
vector Bleh = (-Pd*Pn); | |||
oO = Bleh - (Qn*Cross)/(Qn*Bleh+Qd)*Cross/llVecMag(Cross);} | |||
</source> | |||
} | |||
</ | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
Line 972: | Line 894: | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| vector | | vector Pn | ||
| | | Normal of Plane 1 (unit vector) | ||
|- | |- | ||
| float | | float Pd | ||
| | | Distance of Plane 1 | ||
|- | |- | ||
| vector | | vector Qn | ||
| | | Normal of Plane 2 (unit vector) | ||
|- | |- | ||
| | | float Qd | ||
| | | Distance of Plane 2 | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| | | vector oO | ||
| | | Intersection Line's origin | ||
|- | |||
| vector oD | |||
| Intersection Line's direction | |||
|- | |||
!style="background-color: #eed0d0" colspan="2"| Requirement | |||
|- | |||
|style="background-color: #eed0d0" colspan="2"| global vector oO | |||
|- | |||
|style="background-color: #eed0d0" colspan="2"| global vector oD | |||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
Line 996: | Line 927: | ||
|} | |} | ||
<!--############# PLANE AND RAY, PROJECTION #############--> | |||
<!--############# RAY | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Ray | ==== Plane and Ray, Projection ==== | ||
|- | |- | ||
| | | | ||
Projects a ray onto a plane | |||
< | <source lang="lsl2"> | ||
float | vector oO;vector oD; | ||
</ | gPRpR(vector Pn,float Pd,vector O,vector D){ | ||
oO = O - (Pn * O + Pd) * Pn; | |||
vector t = llVecNorm( D - (Pn*((D*Pn)/(Pn*Pn))) );t = <1.0/t.x,1.0/t.y,1.0/t.z>; | |||
oD = Pn%t;} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
!style="background-color: #d0d0ee" | Input | !style="background-color: #d0d0ee" | Input | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |||
| vector Pn | |||
| Normal of Plane (unit vector) | |||
|- | |||
| float Pd | |||
| Distance of Plane | |||
|- | |- | ||
| vector O | | vector O | ||
Line 1,019: | Line 958: | ||
| vector D | | vector D | ||
| Direction of Ray | | Direction of Ray | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| | | vector oO | ||
| | | Projected Ray Origin | ||
|} | |- | ||
<div style="float:left;font-size: 80%;"> | | vector oD | ||
'''3D'''</div> | | Projected Ray Direction | ||
<div style="float:right;font-size: 80%;"> | |- | ||
!style="background-color: #eed0d0" colspan="2"| Requirement | |||
|- | |||
|style="background-color: #eed0d0" colspan="2"| global vector oO | |||
|- | |||
|style="background-color: #eed0d0" colspan="2"| global vector oD | |||
|} | |||
<div style="float:left;font-size: 80%;"> | |||
'''3D'''</div> | |||
<div style="float:right;font-size: 80%;"> | |||
By Nexii Malthus</div> | By Nexii Malthus</div> | ||
|} | |} | ||
=== | === <div style="font-size: 120%;">[[#Geometric Library|Sphere Functions]]</div> === | ||
<!--############# | <!--############# SPHERE AND RAY, INTERSECTION POINT #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== | ==== Sphere and Ray, Intersection Point ==== | ||
|- | |- | ||
| | | | ||
Finds intersection of | Finds intersection point of sphere and ray | ||
< | <source lang="lsl2"> | ||
vector gSRxX(vector Sp, float Sr, vector Ro, vector Rd){ | |||
float t; Ro -= Sp; | |||
float | if(Rd == ZERO_VECTOR) return ZERO_VECTOR; | ||
float a = Rd * Rd; | |||
float b = 2 * Rd * Ro; | |||
float c = (Ro * Ro) - (Sr * Sr); | |||
float disc = b * b - 4 * a * c; | |||
if(disc < 0) return ZERO_VECTOR; | |||
float distSqrt = llSqrt(disc); | |||
float q; | |||
if( | if(b < 0) | ||
q = (-b - distSqrt)/2.0; | |||
else | |||
q = (-b + distSqrt)/2.0; | |||
float t0 = q / a; | |||
float t1 = c / q; | |||
if(t0 > t1){ | |||
float temp = t0; | |||
t0 = t1; | |||
t1 = temp; | |||
} | } | ||
if( | if(t1 < 0) return ZERO_VECTOR; | ||
if(t0 < 0) | |||
t = t1; | |||
else | |||
t = t0; | |||
return | return Sp + Ro + (t * Rd); | ||
} | } | ||
</ | </source> | ||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
!style="background-color: #d0d0ee" | Input | !style="background-color: #d0d0ee" | Input | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |||
| vector Sp | |||
| Origin of Sphere | |||
|- | |||
| float Sr | |||
| Radius of Sphere | |||
|- | |- | ||
| vector Ro | | vector Ro | ||
Line 1,113: | Line 1,046: | ||
| Direction of Ray | | Direction of Ray | ||
|- | |- | ||
| | !style="background-color: #d0d0ee" | Output | ||
| | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| vector | | vector gSRxX | ||
| Returns intersection point of sphere and ray otherwise ZERO_VECTOR | |||
| Returns | |||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
'''3D'''</div> | '''3D'''</div> | ||
<div style="float:right;font-size: 80%;"> | <div style="float:right;font-size: 80%;"> | ||
By | By Nexii Malthus</div> | ||
|} | |} | ||
<!--############# | <!--############# SPHERE AND RAY, INTERSECTION BOOLEAN #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== | |||
==== Sphere and Ray, Intersection Boolean ==== | |||
|- | |- | ||
| | | | ||
Finds | Finds if there is a intersection of sphere and ray | ||
< | <source lang="lsl2"> | ||
integer gSRx(vector Sp, float Sr, vector Ro, vector Rd){ | |||
float | float t;Ro = Ro - Sp; | ||
if( | //vector RayOrg = llDetectedPos(x) - llGetPos(); | ||
if(Rd == ZERO_VECTOR) return FALSE; | |||
</ | |||
float a = Rd * Rd; | |||
float b = 2 * Rd * Ro; | |||
float c = (Ro * Ro) - (Sr * Sr); | |||
float disc = b * b - 4 * a * c; | |||
if(disc < 0) return FALSE; | |||
return TRUE; | |||
} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
!style="background-color: #d0d0ee" | Input | !style="background-color: #d0d0ee" | Input | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |||
| vector Sp | |||
| Origin of Sphere | |||
|- | |||
| float Sr | |||
| Radius of Sphere | |||
|- | |- | ||
| vector Ro | | vector Ro | ||
Line 1,157: | Line 1,098: | ||
| vector Rd | | vector Rd | ||
| Direction of Ray | | Direction of Ray | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| | | integer gSRx | ||
| Returns | | Returns a boolean indicating if there is a valid intersection | ||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
'''3D'''</div> | '''3D'''</div> | ||
<div style="float:right;font-size: 80%;"> | <div style="float:right;font-size: 80%;"> | ||
By | By Nexii Malthus</div> | ||
|} | |} | ||
<!--############# | === <div style="font-size: 120%;">[[#Geometric Library|Ray Functions]]</div> === | ||
<!--############# RAY AND POINT, PROJECTED DISTANCE #############--> | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== | ==== Ray and Point, projected distance ==== | ||
|- | |- | ||
| | | | ||
Finds | Finds projected distance of a point along a ray | ||
< | <source lang="lsl2"> | ||
float gRXpZ(vector O,vector D,vector A){ | |||
return (A-O)*D;} | |||
</source> | |||
</ | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | {|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | ||
!style="background-color: #d0d0ee" | Input | !style="background-color: #d0d0ee" | Input | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |||
| vector O | |||
| Origin of Ray | |||
|- | |||
| vector D | |||
| Direction of Ray | |||
|- | |- | ||
| vector A | | vector A | ||
| Origin of Point | | Origin of Point | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | |||
!style="background-color: #d0d0ee" | Output | |||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| | | float gRXpZ | ||
| Returns | | Returns projected distance of a point along a ray | ||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
Line 1,228: | Line 1,150: | ||
|} | |} | ||
<!--############# BOX AND | === <div style="font-size: 120%;">[[#Geometric Library|Box Functions]]</div> === | ||
<!--############# BOX AND RAY, INTERSECTION DISTANCE #############--> | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== Box and | ==== Box and Ray, Intersection Distance ==== | ||
|- | |- | ||
| | | | ||
Finds intersection of a Ray to a Box and returns intersection distance, otherwise -1 if there is no legal intersection. | |||
< | <source lang="lsl2"> | ||
vector | float gBRxZ(vector Ro,vector Rd, vector Bo, vector Bs, rotation Br){ | ||
vector eB = 0.5* | vector oB = (Ro-Bo)/Br; vector dB = Rd/Br; vector eB = 0.5*Bs; | ||
float mD = -1.0; float D; vector X; | |||
if(llFabs(dB.x) > 0.000001){ | |||
D = (-eB.x - oB.x ) / dB.x; | |||
if(D >= 0.0){ | |||
X = oB + D * dB; | |||
if(X.y >= -eB.y && X.y <= eB.y && X.z >= -eB.z && X.z <= eB.z) | |||
mD = D; | |||
} | |||
D = ( eB.x - oB.x ) / dB.x; | |||
if (D >= 0.0){ | |||
X = oB + D * dB; | |||
if(X.y >= -eB.y && X.y <= eB.y && X.z >= -eB.z && X.z <= eB.z) | |||
if (mD < 0.0 || mD > D) | |||
mD = D; | |||
} | |||
} | |||
if(llFabs(dB.y) > 0.000001){ | |||
D = (-eB.y - oB.y ) / dB.y; | |||
if(D >= 0.0){ | |||
X = oB + D * dB; | |||
if(X.x >= -eB.x && X.x <= eB.x && X.z >= -eB.z && X.z <= eB.z) | |||
if (mD < 0.0 || mD > D) | |||
mD = D; | |||
if( | } | ||
D = ( eB.y - oB.y ) / dB.y; | |||
if (D >= 0.0){ | |||
X = oB + D * dB; | |||
if(X.x >= -eB.x && X.x <= eB.x && X.z >= -eB.z && X.z <= eB.z) | |||
if (mD < 0.0 || mD > D) | |||
mD = D; | |||
} | |||
} | } | ||
if(llFabs(dB.z) > 0.000001){ | |||
D = (-eB.z - oB.z ) / dB.z; | |||
if(D >= 0.0){ | |||
X = oB + D * dB; | |||
if(X.x >= -eB.x && X.x <= eB.x && X.y >= -eB.y && X.y <= eB.y) | |||
if (mD < 0.0 || mD > D) | |||
mD = D; | |||
} | |||
D = ( eB.z - oB.z ) / dB.z; | |||
if (D >= 0.0){ | |||
X = oB + D * dB; | |||
if(X.x >= -eB.x && X.x <= eB.x && X.y >= -eB.y && X.y <= eB.y) | |||
if (mD < 0.0 || mD > D) | |||
mD = D; | |||
} | |||
} | } | ||
return mD; | |||
} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
</ | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | !style="background-color: #d0d0ee" | Input | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| vector | | vector Ro | ||
| Origin of | | Origin of Ray | ||
|- | |||
| vector Rd | |||
| Direction of Ray | |||
|- | |- | ||
| vector Bo | | vector Bo | ||
Line 1,304: | Line 1,240: | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| | | float gBRxZ | ||
| Returns | | Returns distance to intersection of a ray and a box | ||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
'''3D'''</div> | '''3D'''</div> | ||
<div style="float:right;font-size: 80%;"> | <div style="float:right;font-size: 80%;"> | ||
By | By [http://forums.secondlife.com/showpost.php?p=1984100&postcount=7 Hewee Zetkin]</div> | ||
|} | |} | ||
<!--############# BOX AND RAY, INTERSECTION POINT #############--> | |||
<!--############# | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== | ==== Box and Ray, Intersection Point ==== | ||
|- | |- | ||
| | | | ||
Finds intersection of a Ray to a Box and returns intersection point, otherwise ZERO_VECTOR if there is no legal intersection. | |||
< | <source lang="lsl2"> | ||
vector gBRxX( vector Ro, vector Rd, vector Bo, vector Bs, rotation Br){ | |||
float k = gBRxZ(Ro,Rd,Bo,Bs,Br); | |||
if( k != -1.0 ) return Ro + Rd * k; | |||
else return ZERO_VECTOR;} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| vector Ro | |||
| Origin of Ray | |||
|- | |||
| vector Rd | |||
| Direction of Ray | |||
|- | |||
| vector Bo | |||
} | | Origin of Box | ||
</ | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |- | ||
| | | vector Bs | ||
| | | Size of Box | ||
|- | |- | ||
| | | rotation Br | ||
| | | Rotation of Box | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| | | vector gBRxX | ||
| Returns | | Returns point of intersection of a ray and a box | ||
|- | |||
!style="background-color: #eed0d0" colspan="2"| Requirement | |||
|- | |||
|style="background-color: #eed0d0" colspan="2"| float gBRxZ(vector Ro,vector Rd, vector Bo, vector Bs, rotation Br) | |||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
''' | '''3D'''</div> | ||
<div style="float:right;font-size: 80%;"> | <div style="float:right;font-size: 80%;"> | ||
By [http://forums.secondlife.com/showpost.php?p=1984100&postcount=7 Hewee Zetkin]</div> | |||
|} | |} | ||
<!--############# | <!--############# BOX AND POINT, INTERSECTION BOOLEAN #############--> | ||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== | |||
==== Box and Point, Intersection Boolean ==== | |||
|- | |- | ||
| | | | ||
Finds if there is an intersection of a Point and a Box and returns boolean | |||
< | <source lang="lsl2"> | ||
integer | integer gBXx(vector A, vector Bo, vector Bs, rotation Br){ | ||
vector eB = 0.5*Bs; vector rA = (A-Bo)/Br; | |||
return (rA.x<eB.x && rA.x>-eB.x && rA.y<eB.y && rA.y>-eB.y && rA.z<eB.z && rA.z>-eB.z); } | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | |||
} | |||
</ | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |- | ||
| | | vector A | ||
| | | Origin of Point | ||
|- | |||
| vector Bo | |||
| Origin of Box | |||
|- | |||
| vector Bs | |||
| Size of Box | |||
|- | |- | ||
| | | rotation Br | ||
| | | Rotation of Box | ||
|- | |- | ||
!style="background-color: #d0d0ee" | Output | !style="background-color: #d0d0ee" | Output | ||
!style="background-color: #d0d0ee" | Description | !style="background-color: #d0d0ee" | Description | ||
|- | |- | ||
| integer | | integer gBXx(vector A, vector Bo, vector Bs, rotation Br) | ||
| Returns | | Returns boolean check of intersection of a point and a box if there is one, otherwise FALSE | ||
|} | |} | ||
<div style="float:left;font-size: 80%;"> | <div style="float:left;font-size: 80%;"> | ||
''' | '''3D'''</div> | ||
<div style="float:right;font-size: 80%;"> | <div style="float:right;font-size: 80%;"> | ||
By Nexii Malthus</div> | |||
|} | |} | ||
<!--############# BOX AND POINT, NEAREST POINT ON EDGE #############--> | |||
<!--############# | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | !style="color: #000000; background-color: #aaaaff;" height="20px"| | ||
==== | |||
==== Box and Point, Nearest Point on Edge ==== | |||
|- | |- | ||
| | | | ||
Processes point on nearest edge of box to given point | |||
< | <source lang="lsl2"> | ||
vector | vector gBXnEX(vector A, vector Bo, vector Bs, rotation Br){ | ||
vector eB = 0.5*<llFabs(Bs.x),llFabs(Bs.y),llFabs(Bs.z)>; | |||
< | vector rA = (A-Bo)/Br; | ||
float mD = 3.402823466E+38; | |||
vector X; | |||
! | list EdgesX = [< 0, eB.y, eB.z>, < 0,-eB.y, eB.z>, < 0,-eB.y,-eB.z>, < 0, eB.y,-eB.z>]; | ||
list EdgesY = [< eB.x, 0, eB.z>, <-eB.x, 0, eB.z>, <-eB.x, 0,-eB.z>, < eB.x, 0,-eB.z>]; | |||
list EdgesZ = [< eB.x, eB.y, 0>, <-eB.x, eB.y, 0>, <-eB.x,-eB.y, 0>, < eB.x,-eB.y, 0>]; | |||
integer x = (EdgesX != []); | |||
while( x-- ){ | |||
float y = gLXdZ( llList2Vector( EdgesX, x ), <1,0,0>, rA ); | |||
! | if( rA.x > eB.x ) y += rA.x - eB.x; | ||
else if( rA.x < -eB.x ) y -= rA.x - -eB.x; | |||
if( y < mD ){ mD = y; X = gLXnX( llList2Vector( EdgesX, x ), <1,0,0>, rA ); } | |||
} | |||
x = (EdgesY != []); | |||
< | while( x-- ){ | ||
float y = gLXdZ( llList2Vector( EdgesY, x ), <0,1,0>, rA ); | |||
< | |||
if( rA.y > eB.y ) y += rA.y - eB.y; | |||
else if( rA.y < -eB.y ) y -= rA.y - -eB.y; | |||
if( y < mD ){ mD = y; X = gLXnX( llList2Vector( EdgesY, x ), <0,1,0>, rA ); } | |||
} | |||
x = (EdgesZ != []); | |||
while( x-- ){ | |||
float y = gLXdZ( llList2Vector( EdgesZ, x ), <0,0,1>, rA ); | |||
if( rA.z > eB.z ) y += rA.z - eB.z; | |||
else if( rA.z < -eB.z ) y -= rA.z - -eB.z; | |||
if( y < mD ){ mD = y; X = gLXnX( llList2Vector( EdgesZ, x ), <0,0,1>, rA ); } | |||
} | |||
if( mD < 0.000001 ) return <-1,-1,-1>; | |||
if( X.x > eB.x ) X.x = eB.x; | |||
else if( X.x < -eB.x ) X.x = -eB.x; | |||
if( X.y > eB.y ) X.y = eB.y; | |||
else if( X.y < -eB.y ) X.y = -eB.y; | |||
if( X.z > eB.z ) X.z = eB.z; | |||
else if( X.z < -eB.z ) X.z = -eB.z; | |||
return Bo + ( X * Br );} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| vector A | |||
| Origin of Point | |||
|- | |||
| vector Bo | |||
| Origin of Box | |||
|- | |||
| vector Bs | |||
| Size of Box | |||
|- | |||
| rotation Br | |||
| Rotation of Box | |||
|- | |||
!style="background-color: #d0d0ee" | Output | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| vector gBXnEX(vector A, vector Bo, vector Bs, rotation Br) | |||
| Returns nearest point on edge of box B closest to point A. Returns <-1,-1,-1> if already on closest point. | |||
|- | |||
!style="background-color: #eed0d0" colspan="2"| Requirement | |||
|- | |||
|style="background-color: #eed0d0" colspan="2"| float gLXdZ(vector O,vector D,vector A) | |||
|- | |||
|style="background-color: #eed0d0" colspan="2"| vector gLXdV(vector O,vector D,vector A) | |||
|- | |||
|style="background-color: #eed0d0" colspan="2"| vector gLXnX(vector O,vector D,vector A) | |||
|} | |||
<div style="float:left;font-size: 80%;"> | |||
'''3D'''</div> | |||
<div style="float:right;font-size: 80%;"> | |||
By Nexii Malthus</div> | |||
|} | |||
=== <div style="font-size: 120%;">[[#Geometric Library|Cylinder]]</div> === | |||
=== | |||
For anyone curious to the shorthand used and who wish to use a lookup table can use this as a reference. Or anyone who wishes to add a new function to the library is welcome to but it would be recommended to keep consistency. | <!--############# CYLINDER AND POINT, INTERSECTION BOOLEAN #############--> | ||
I tried to minimize the script function names to be easily readable. All the geometric function names start with a g. | {|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | ||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | |||
''g'' ('''Shape1''') ('''Shape2''') ('''Process''') ('''Return''' (''Only needed if other than integer'')) | |||
==== Cylinder and Point, Intersection Boolean ==== | |||
Here is the legend: | |- | ||
| | |||
{| class="sortable" {{Prettytable}} | Finds if there is an intersection of a Point and a Cylinder and returns boolean | ||
|-{{Hl2}} | <source lang="lsl2"> | ||
! '''Shorthand''' | integer gCXx( vector A, vector O, rotation R, vector S ) { | ||
! '''Name''' | A = ( A - O ) / R;// Converts to local object frame | ||
return (llPow(A.x/S.x*2,2) + llPow(A.y/S.y*2,2)) <= 1. // Test radius | |||
&& llFabs(A.z/S.z*2) <= 1.;// Test top/bottom | |||
} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| vector A | |||
| Origin of Point | |||
|- | |||
| vector Bo | |||
| Origin of Cylinder | |||
|- | |||
| vector Bs | |||
| Size of Cylinder | |||
|- | |||
| rotation Br | |||
| Rotation of Cylinder | |||
|- | |||
!style="background-color: #d0d0ee" | Output | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| integer gCXx( vector A, vector O, rotation R, vector S ) | |||
| Returns boolean check of intersection of a point and a cylinder if there is one, otherwise FALSE | |||
|} | |||
<div style="float:left;font-size: 80%;"> | |||
'''3D'''</div> | |||
<div style="float:right;font-size: 80%;"> | |||
By Nexii Malthus</div> | |||
|} | |||
=== <div style="font-size: 120%;">[[#Geometric Library|Polygon]]</div> === | |||
<!--############# Polygon and Point, Intersection Boolean #############--> | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | |||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | |||
==== Polygon and Point, Intersection Boolean ==== | |||
|- | |||
| | |||
Figures out if point is inside of polygon or otherwise. | |||
<source lang="lsl2"> | |||
integer gCPXx( list CP, vector X ) | |||
{//Copyright (c) 1970-2003, Wm. Randolph Franklin; 2008, Strife Onizuka | |||
integer i = ~(CP != []); | |||
integer c = 0; | |||
if(i < -2){ | |||
vector vi = llList2Vector(CP, -1); | |||
do { | |||
vector vj = vi; | |||
vi = llList2Vector(CP, i); | |||
if((vi.y > X.y) ^ (vj.y > X.y)){ | |||
if(vj.y != vi.y) | |||
c = c ^ (X.x < (((vj.x - vi.x) * (X.y - vi.y) / (vj.y - vi.y)) + vi.x)); | |||
else c = c ^ (0 < ((vj.x-vi.x) * (X.y-vi.y))); | |||
} | |||
} while (++i); | |||
} | |||
return c; | |||
} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| list CP | |||
| Vertices of Concave Polygon | |||
|- | |||
| vector X | |||
| Origin of Point | |||
|- | |||
!style="background-color: #d0d0ee" | Output | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| integer gCPXx( list CP, vector X ) | |||
| Returns TRUE if point (X) intersects concave polygon (CP), otherwise FALSE | |||
|} | |||
<div style="float:left;font-size: 80%;"> | |||
'''2D'''</div> | |||
<div style="float:right;font-size: 80%;"> | |||
Copyright (c) 1970-2003, Wm. Randolph Franklin (Must accept [[#.231|License #1]]), LSL-Port By Strife Onizuka</div> | |||
|} | |||
<!--############# Polygon and Line Segment, Intersection Boolean #############--> | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | |||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | |||
==== Polygon and Line Segment, Intersection Boolean ==== | |||
|- | |||
| | |||
Figures out if line segment intersects with polygon. | |||
<source lang="lsl2"> | |||
integer gVPLSx( vector P0, vector P1, list VP ){ | |||
//Copyright 2001, softSurfer (www.softsurfer.com); 2008, Nexii Malthus | |||
if( P0 == P1 ) return gCPXx( VP, P0 ); | |||
float tE = 0; float tL = 1; | |||
float t; float N; float D; | |||
vector dS = P1 - P0; | |||
vector e; integer x; integer y = VP!=[]; | |||
@start; | |||
for( x = 0; x < y; ++x ){ | |||
e = llList2Vector( VP, x+1 ) - llList2Vector( VP, x ); | |||
N = Perp( e, P0 - llList2Vector( VP, x ) ); | |||
D = -Perp( e, dS ); | |||
if( llFabs(D) < 0.00000001 ) | |||
if( N < 0 ) return FALSE; | |||
else jump start; | |||
t = N / D; | |||
if( D < 0 ){ | |||
if( t > tE ){ tE = t; if( tE > tL ) return FALSE; } | |||
} else { | |||
if( t < tL ){ tL = t; if( tL < tE ) return FALSE; } | |||
} } | |||
// PointOfEntrance = P0 + tE * dS; | |||
// PointOfExit = P0 + tL * dS; | |||
return TRUE; | |||
} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| list VP | |||
| Vertices of Convex Polygon | |||
|- | |||
| vector P0, vector P1 | |||
| Start and End of Line Segment | |||
|- | |||
!style="background-color: #d0d0ee" | Output | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| integer gVPLSx( vector P0, vector P1, list VP ) | |||
| Returns TRUE if line segment (P0,P1) intersects convex polygon (VP), otherwise FALSE | |||
|- | |||
!style="background-color: #eed0d0" colspan="2"| Requirement | |||
|- | |||
|style="background-color: #eed0d0" | <source lang="lsl2">float Perp( vector U, vector V ){ return U.x*V.y - U.y*V.x; }</source> | |||
| Perpendicular dot product | |||
|- | |||
|style="background-color: #eed0d0" | integer gCPXx( list CP, vector X ) | |||
| Only needed for (P0 == P1) safety catch check, so optional | |||
|} | |||
<div style="float:left;font-size: 80%;"> | |||
'''2D'''</div> | |||
<div style="float:right;font-size: 80%;"> | |||
Copyright 2001, softSurfer (www.softsurfer.com) (Must accept [[#.232|License #2]]), LSL-Port By Nexii Malthus</div> | |||
|} | |||
=== <div style="font-size: 120%;">[[#Geometric Library|Other Functions]]</div> === | |||
<!--############# 3D PROJECTION #############--> | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | |||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | |||
==== 3D Projection ==== | |||
|- | |||
| | |||
Projects a vector A by vector B. | |||
<source lang="lsl2"> | |||
vector Project3D(vector A,vector B){ | |||
return B * ( ( A * B ) / ( B * B ) );} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| vector A | |||
| First Vector | |||
|- | |||
| vector B | |||
| Second Vector | |||
|- | |||
!style="background-color: #d0d0ee" | Output | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| return Project3D(vector A, vector B) | |||
| Returns result of projection | |||
|} | |||
<div style="float:left;font-size: 80%;"> | |||
'''3D'''</div> | |||
<div style="float:right;font-size: 80%;"> | |||
By Nexii Malthus</div> | |||
|} | |||
<!--############# REFLECTION #############--> | |||
{|cellspacing="0" cellpadding="3" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #ffffff; border-collapse: collapse" width="80%" | |||
!style="color: #000000; background-color: #aaaaff;" height="20px"| | |||
==== Reflection ==== | |||
|- | |||
| | |||
Reflects Ray R with surface normal N | |||
<source lang="lsl2"> | |||
vector Reflect(vector R,vector N){ | |||
return R - 2 * N * ( R * N );} | |||
</source> | |||
{|cellspacing="0" cellpadding="6" border="1" style="border: 1px solid #aaaaaa; margin: 1em 1em 1em 0pt; background-color: #e0e0ff; border-collapse: collapse" | |||
!style="background-color: #d0d0ee" | Input | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| vector R | |||
| Ray Normal | |||
|- | |||
| vector N | |||
| Surface Normal | |||
|- | |||
!style="background-color: #d0d0ee" | Output | |||
!style="background-color: #d0d0ee" | Description | |||
|- | |||
| return Reflect(vector R, vector N) | |||
| Returns result of reflection | |||
|} | |||
<div style="float:left;font-size: 80%;"> | |||
'''3D'''</div> | |||
<div style="float:right;font-size: 80%;"> | |||
By Nexii Malthus</div> | |||
|} | |||
=== <div style="font-size: 120%;">[[#Geometric Library|Glossary]]</div> === | |||
For anyone curious to the shorthand used and who wish to use a lookup table can use this as a reference. Or anyone who wishes to add a new function to the library is welcome to but it would be recommended to keep consistency. | |||
I tried to minimize the script function names to be easily readable. All the geometric function names start with a g. | |||
''g'' ('''Shape1''') ('''Shape2''') ('''Process''') ('''Return''' (''Only needed if other than integer'')) | |||
Here is the legend: | |||
{| class="sortable" {{Prettytable}} | |||
|-{{Hl2}} | |||
! '''Shorthand''' | |||
! '''Name''' | |||
! class="unsortable" | '''Description''' | ! class="unsortable" | '''Description''' | ||
|- | |- | ||
! colspan="3" height="50%" | Geometric Types, all the shapes in the library | ! colspan="3" height="50%" | Geometric Types, all the shapes in the library | ||
|- | |- | ||
||X | ||X | ||
||Point | ||Point | ||
||vector defining a point in space | ||vector defining a point in space | ||
|- | |- | ||
||L | ||L | ||
||'''L'''ine | ||'''L'''ine | ||
||A line has an origin and a direction and is infinitely long | ||A line has an origin and a direction and is infinitely long | ||
|- | |- | ||
||LS | ||LS | ||
||'''L'''ine '''S'''egment | ||'''L'''ine '''S'''egment | ||
||A line segment is a finite line and therefore consists of a start and end position | ||A line segment is a finite line and therefore consists of a start and end position | ||
|- | |- | ||
||R | ||R | ||
||'''R'''ay | ||'''R'''ay | ||
||A ray is like a line, except it is more distinct as it defines wether it points forward or back | ||A ray is like a line, except it is more distinct as it defines wether it points forward or back | ||
|- | |- | ||
||P | ||P | ||
||'''P'''lane | ||'''P'''lane | ||
||A 2D doubly ruled surface of infinite size | ||A 2D doubly ruled surface of infinite size | ||
|- | |- | ||
||S | ||S | ||
||'''S'''phere | ||'''S'''phere | ||
||A sphere is defined by origin and radius | ||A sphere is defined by origin and radius (No ellipsoid functions available yet) | ||
|- | |- | ||
||B | ||B | ||
||'''B'''ox | ||'''B'''ox | ||
||A box is six sided and defined by origin, size as well as a rotation. | ||A box primitive is six sided and defined by origin, size as well as a rotation. | ||
|- | |||
||C | |||
||'''C'''ylinder | |||
||An elliptic cylinder primitive . | |||
|- | |- | ||
||VP | ||VP | ||
Line 1,573: | Line 1,770: | ||
|} | |} | ||
=== Licenses === | === <div style="font-size: 120%;">[[#Geometric Library|Licenses]]</div> === | ||
==== #1 ==== | ==== #1 ==== | ||
< | <source lang="lsl2"> | ||
//Copyright (c) 1970-2003, Wm. Randolph Franklin | //Copyright (c) 1970-2003, Wm. Randolph Franklin | ||
//Copyright (c) 2008, Strife Onizuka (porting to LSL) | //Copyright (c) 2008, Strife Onizuka (porting to LSL) | ||
Line 1,603: | Line 1,800: | ||
//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | //OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | ||
//SOFTWARE. | //SOFTWARE. | ||
</ | </source> | ||
==== #2 ==== | ==== #2 ==== | ||
< | <source lang="lsl2"> | ||
// Copyright 2001, softSurfer (www.softsurfer.com); 2008, LSL-port by Nexii Malthus | // Copyright 2001, softSurfer (www.softsurfer.com); 2008, LSL-port by Nexii Malthus | ||
// This code may be freely used and modified for any purpose | // This code may be freely used and modified for any purpose | ||
Line 1,613: | Line 1,810: | ||
// liable for any real or imagined damage resulting from its use. | // liable for any real or imagined damage resulting from its use. | ||
// Users of this code must verify correctness for their application. | // Users of this code must verify correctness for their application. | ||
</ | </source> |
Latest revision as of 20:00, 24 January 2015
LSL Portal | Functions | Events | Types | Operators | Constants | Flow Control | Script Library | Categorized Library | Tutorials |
Please vote for: https://jira.secondlife.com/browse/WEB-235 So that I can expand each function into deeper detail without the page starting to fail in readability. --Nexii Malthus 23:05, 24 October 2008 (UTC)
:Break it up so each major section has its own page... thats why hypertext was invented. -Overbrain Unplugged 13:36, 10 October 2010 (UTC)
Geometric Library
Line and Point, Vector | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Calculates the vector from a point 'to' the closest point on a line vector gLXdV(vector O,vector D,vector A){
return (O-A)-((O-A)*D)*D;}
3D
By Nexii Malthus
|
Line and Point, Distance | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Calculates distance of line to point, same as measuring magnitude of Line and Point Vector, but faster on it's own float gLXdZ(vector O,vector D,vector A){
vector k = ( A - O ) % D;
return llSqrt( k * k );}
3D
By Nexii Malthus
|
Line Nearest Point, Nearest Point | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Returns nearest point on line to given point vector gLXnX(vector O,vector D,vector A){
return gLXdV(O,D,A) + A;}
3D
By Nexii Malthus
|
Line and Line, Vector | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Shortest vector of two lines vector gLLdV(vector O1,vector D1,vector O2,vector D2){
vector A = O2 - O1; vector B = D1 % D2;
return B*( (A*B)/(B*B) );}
3D
By Nexii Malthus
|
Line and Line, Distance | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Returns the distance between two lines float gLLdZ(vector O1,vector D1,vector O2,vector D2){
vector A = D1%D2;float B = llVecMag(A);A = <A.x/B,A.y/B,A.z/B>;
return (O2-O1) * A;}
3D
By Nexii Malthus
|
Line and Line, Nearest point | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Closest point of two lines vector gLLnX(vector O1,vector D1,vector O2,vector D2){
vector nO1 = < O1*D1, O1*D2, 0>;
vector nO2 = < O2*D1, O2*D2, 0>;
vector nD1 = < D1*D1, O1*D2, 0>;
vector nD2 = < O2*D1, O2*D2, 0>;
float t = ( nD2.x*nD1.y - nD1.x*nD2.y );
t = ( nD2.y*(nO1.x-nO2.x) - nD2.x*(nO1.y-nO2.y) ) / t;
return O1 + D1*t;}
2D
By Nexii Malthus
|
Line and Line, intersection point | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Computes intersection point of two lines, if there is any, else <-1,-1,-1> if none. vector gLLxX( vector A, vector B, vector C, vector D ){
vector b = B-A; vector d = D-C;
float dotperp = b.x*d.y - b.y*d.x;
if (dotperp == 0) return <-1,-1,-1>;
vector c = C-A;
float t = (c.x*d.y - c.y*d.x) / dotperp;
return <A.x + t*b.x, A.y + t*b.y, 0>;}
2D
By Nexii Malthus
|
Line and Line, two nearest points of lines | ||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Two closest points of two lines on each line vector X1;vector X2;
gLLnnXX(vector O1,vector D1,vector O2,vector D2){
vector nO1 = < O1*D1, O1*D2, 0>;
vector nO2 = < O2*D1, O2*D2, 0>;
vector nD1 = < D1*D1, O1*D2, 0>;
vector nD2 = < O2*D1, O2*D2, 0>;
float t = ( nD2.x*nD1.y - nD1.x*nD2.y );
t = ( nD2.y*(nO1.x-nO2.x) - nD2.x*(nO1.y-nO2.y) ) / t;
X1 = O1 + D1*t;
X2 = X1 + nD1%nD2;}
2D
By Nexii Malthus
|
Line and Line, nearest line | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Input two lines, the function will return a list containing two vectors responding to the line nearest between them. As well as two floats corresponding to the scalar value on the two line of where the line has an end located at. list gLLnL( vector v0, vector v1, vector v2, vector v3 ) {
float Eps = 0.000001; vector vx; vector vy; vector va; vector vb; vector vc;
float x; float y; float d0; float d1; float d2; float d3; float d4;
va = v0-v2; vb = v3-v2; if(llVecMag(vb)<Eps) return [];
vc = v1-v0; if(llVecMag(vc)<Eps) return [];
d0 = va*vb; d1 = vb*vc; d2 = va*vc; d3 = vb*vb; d4 = vc*vc;
float den = d4*d3-d1*d1; if( llFabs(den) < Eps ) return [];
float num = d0*d1-d2*d3; x = num/den; y = (d0+d1*x)/d3;
vx = v0+vc*x; vy = v2+vb*y; return [vx,vy,x,y]; }
3D
By Nexii Malthus
|
Line and Line Segments, nearest line segment | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Input two line segments, the function will return a list containing two vectors responding to the line segment nearest between them. As well as two floats corresponding to the scalar value on the two line segments of where the line segment has an end located at. list gLSLSnLS( vector v0, vector v1, vector v2, vector v3 ) {
float Eps = 0.000001; vector vx; vector vy; vector va; vector vb; vector vc;
float x; float y; float d0; float d1; float d2; float d3; float d4;
va = v0-v2; vb = v3-v2; if(llVecMag(vb)<Eps) return [];
vc = v1-v0; if(llVecMag(vc)<Eps) return [];
if( llFabs(vc.x + vc.y + vc.z) < Eps ) return [];
d0 = va*vb; d1 = vb*vc; d2 = va*vc; d3 = vb*vb; d4 = vc*vc;
float den = d4*d3-d1*d1; if( llFabs(den) < Eps ) return [];
float num = d0*d1-d2*d3; x = num/den; y = (d0+d1*x)/d3;
if(x<0)x=0; else if(x>1)x=1; if(y<0)y=0; else if(y>1)y=1;
vx = v0+vc*x; vy = v2+vb*y; return [vx,vy,x,y]; }
3D
By Nexii Malthus
|
Line and Line, two nearest points with vector and distance | ||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Computes two closest points of two lines, vector and distance vector X1;vector X2;vector V1;float Z1;
gLLnnXXVZ(vector O1,vector D1,vector O2,vector D2){
vector nO1 = < O1*D1, O1*D2, 0>;
vector nO2 = < O2*D1, O2*D2, 0>;
vector nD1 = < D1*D1, O1*D2, 0>;
vector nD2 = < O2*D1, O2*D2, 0>;
float t = ( nD2.x*nD1.y - nD1.x*nD2.y );
t = ( nD2.y*(nO1.x-nO2.x) - nD2.x*(nO1.y-nO2.y) ) / t;
X1 = O1 + D1*t;
X2 = X1 + CP(nD1,nD2);
V1 = nD1%nD2;
Z1 = llVecMag(V1);}
2D
By Nexii Malthus
|
Line and Point, Direction | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Works out where point (X) is relative to the line of the segment (L0, L1). float gLSPdir( vector L0, vector L1, vector X ){
return (L1.x - L0.x)*(X.y - L0.y) - (X.x - L0.x)*(L1.y - L0.y);
}
2D
Copyright 2001, softSurfer (www.softsurfer.com) (Must accept License #2), LSL-Port By Nexii Malthus
|
Plane and Point, Distance | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds distance of a point from a plane float gPXdZ(vector Pn,float Pd,vector A){
return A * Pn + Pd;}
3D
By Nexii Malthus
|
Plane and Point, Vector | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds vector that points from point to nearest on plane vector gPXdV(vector Pn,float Pd,vector A){
return -(Pn * A + Pd)*Pn;}
3D
By Nexii Malthus
|
Plane and Point, Nearest point | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds closest point on plane given point vector gPXnX(vector Pn,float Pd,vector A){
return A - (Pn * A + Pd) * Pn;}
3D
By Nexii Malthus
|
Plane and Ray, Intersection Distance | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds distance to intersection of plane along ray float gPRxZ(vector Pn,float Pd,vector O,vector D){
return -((Pn*O+Pd)/(Pn*D));}
3D
By Nexii Malthus
|
Plane and Ray, Vector | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds distance vector along a ray to a plane vector gPRdV(vector Pn,float Pd,vector O,vector D){
return D * gPRxZ(Pn,Pd,O,D);}
3D
By Nexii Malthus
|
Plane and Ray, Intersection Point | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds intersection point along a ray to a plane vector gPRxX(vector Pn,float Pd,vector O,vector D){
return O + gPRdV(Pn,Pd,O,D);}
3D
By Nexii Malthus
|
Plane and Line, Intersection Point | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds interesection point of a line and a plane vector gPLxX(vector Pn,float Pd,vector O,vector D){
return O + D*-( (Pn*O-Pd)/(Pn*D) );}
3D
By Nexii Malthus
|
Plane and Plane, Intersection Line | ||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds line of intersection of two planes vector oO;vector oD;
gPPxL(vector Pn,float Pd,vector Qn,float Qd){
oD = (Pn%Qn)/llVecMag(Pn%Qn);
vector Cross = (Pn%Qn)%Pn;
vector Bleh = (-Pd*Pn);
oO = Bleh - (Qn*Cross)/(Qn*Bleh+Qd)*Cross/llVecMag(Cross);}
3D
By Nexii Malthus
|
Plane and Ray, Projection | ||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Projects a ray onto a plane vector oO;vector oD;
gPRpR(vector Pn,float Pd,vector O,vector D){
oO = O - (Pn * O + Pd) * Pn;
vector t = llVecNorm( D - (Pn*((D*Pn)/(Pn*Pn))) );t = <1.0/t.x,1.0/t.y,1.0/t.z>;
oD = Pn%t;}
3D
By Nexii Malthus
|
Sphere and Ray, Intersection Point | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds intersection point of sphere and ray vector gSRxX(vector Sp, float Sr, vector Ro, vector Rd){
float t; Ro -= Sp;
if(Rd == ZERO_VECTOR) return ZERO_VECTOR;
float a = Rd * Rd;
float b = 2 * Rd * Ro;
float c = (Ro * Ro) - (Sr * Sr);
float disc = b * b - 4 * a * c;
if(disc < 0) return ZERO_VECTOR;
float distSqrt = llSqrt(disc);
float q;
if(b < 0)
q = (-b - distSqrt)/2.0;
else
q = (-b + distSqrt)/2.0;
float t0 = q / a;
float t1 = c / q;
if(t0 > t1){
float temp = t0;
t0 = t1;
t1 = temp;
}
if(t1 < 0) return ZERO_VECTOR;
if(t0 < 0)
t = t1;
else
t = t0;
return Sp + Ro + (t * Rd);
}
3D
By Nexii Malthus
|
Sphere and Ray, Intersection Boolean | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds if there is a intersection of sphere and ray integer gSRx(vector Sp, float Sr, vector Ro, vector Rd){
float t;Ro = Ro - Sp;
//vector RayOrg = llDetectedPos(x) - llGetPos();
if(Rd == ZERO_VECTOR) return FALSE;
float a = Rd * Rd;
float b = 2 * Rd * Ro;
float c = (Ro * Ro) - (Sr * Sr);
float disc = b * b - 4 * a * c;
if(disc < 0) return FALSE;
return TRUE;
}
3D
By Nexii Malthus
|
Ray and Point, projected distance | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds projected distance of a point along a ray float gRXpZ(vector O,vector D,vector A){
return (A-O)*D;}
3D
By Nexii Malthus
|
Box and Ray, Intersection Distance | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds intersection of a Ray to a Box and returns intersection distance, otherwise -1 if there is no legal intersection. float gBRxZ(vector Ro,vector Rd, vector Bo, vector Bs, rotation Br){
vector oB = (Ro-Bo)/Br; vector dB = Rd/Br; vector eB = 0.5*Bs;
float mD = -1.0; float D; vector X;
if(llFabs(dB.x) > 0.000001){
D = (-eB.x - oB.x ) / dB.x;
if(D >= 0.0){
X = oB + D * dB;
if(X.y >= -eB.y && X.y <= eB.y && X.z >= -eB.z && X.z <= eB.z)
mD = D;
}
D = ( eB.x - oB.x ) / dB.x;
if (D >= 0.0){
X = oB + D * dB;
if(X.y >= -eB.y && X.y <= eB.y && X.z >= -eB.z && X.z <= eB.z)
if (mD < 0.0 || mD > D)
mD = D;
}
}
if(llFabs(dB.y) > 0.000001){
D = (-eB.y - oB.y ) / dB.y;
if(D >= 0.0){
X = oB + D * dB;
if(X.x >= -eB.x && X.x <= eB.x && X.z >= -eB.z && X.z <= eB.z)
if (mD < 0.0 || mD > D)
mD = D;
}
D = ( eB.y - oB.y ) / dB.y;
if (D >= 0.0){
X = oB + D * dB;
if(X.x >= -eB.x && X.x <= eB.x && X.z >= -eB.z && X.z <= eB.z)
if (mD < 0.0 || mD > D)
mD = D;
}
}
if(llFabs(dB.z) > 0.000001){
D = (-eB.z - oB.z ) / dB.z;
if(D >= 0.0){
X = oB + D * dB;
if(X.x >= -eB.x && X.x <= eB.x && X.y >= -eB.y && X.y <= eB.y)
if (mD < 0.0 || mD > D)
mD = D;
}
D = ( eB.z - oB.z ) / dB.z;
if (D >= 0.0){
X = oB + D * dB;
if(X.x >= -eB.x && X.x <= eB.x && X.y >= -eB.y && X.y <= eB.y)
if (mD < 0.0 || mD > D)
mD = D;
}
}
return mD;
}
3D
By Hewee Zetkin
|
Box and Ray, Intersection Point | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds intersection of a Ray to a Box and returns intersection point, otherwise ZERO_VECTOR if there is no legal intersection. vector gBRxX( vector Ro, vector Rd, vector Bo, vector Bs, rotation Br){
float k = gBRxZ(Ro,Rd,Bo,Bs,Br);
if( k != -1.0 ) return Ro + Rd * k;
else return ZERO_VECTOR;}
3D
By Hewee Zetkin
|
Box and Point, Intersection Boolean | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds if there is an intersection of a Point and a Box and returns boolean integer gBXx(vector A, vector Bo, vector Bs, rotation Br){
vector eB = 0.5*Bs; vector rA = (A-Bo)/Br;
return (rA.x<eB.x && rA.x>-eB.x && rA.y<eB.y && rA.y>-eB.y && rA.z<eB.z && rA.z>-eB.z); }
3D
By Nexii Malthus
|
Box and Point, Nearest Point on Edge | ||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Processes point on nearest edge of box to given point vector gBXnEX(vector A, vector Bo, vector Bs, rotation Br){
vector eB = 0.5*<llFabs(Bs.x),llFabs(Bs.y),llFabs(Bs.z)>;
vector rA = (A-Bo)/Br;
float mD = 3.402823466E+38;
vector X;
list EdgesX = [< 0, eB.y, eB.z>, < 0,-eB.y, eB.z>, < 0,-eB.y,-eB.z>, < 0, eB.y,-eB.z>];
list EdgesY = [< eB.x, 0, eB.z>, <-eB.x, 0, eB.z>, <-eB.x, 0,-eB.z>, < eB.x, 0,-eB.z>];
list EdgesZ = [< eB.x, eB.y, 0>, <-eB.x, eB.y, 0>, <-eB.x,-eB.y, 0>, < eB.x,-eB.y, 0>];
integer x = (EdgesX != []);
while( x-- ){
float y = gLXdZ( llList2Vector( EdgesX, x ), <1,0,0>, rA );
if( rA.x > eB.x ) y += rA.x - eB.x;
else if( rA.x < -eB.x ) y -= rA.x - -eB.x;
if( y < mD ){ mD = y; X = gLXnX( llList2Vector( EdgesX, x ), <1,0,0>, rA ); }
}
x = (EdgesY != []);
while( x-- ){
float y = gLXdZ( llList2Vector( EdgesY, x ), <0,1,0>, rA );
if( rA.y > eB.y ) y += rA.y - eB.y;
else if( rA.y < -eB.y ) y -= rA.y - -eB.y;
if( y < mD ){ mD = y; X = gLXnX( llList2Vector( EdgesY, x ), <0,1,0>, rA ); }
}
x = (EdgesZ != []);
while( x-- ){
float y = gLXdZ( llList2Vector( EdgesZ, x ), <0,0,1>, rA );
if( rA.z > eB.z ) y += rA.z - eB.z;
else if( rA.z < -eB.z ) y -= rA.z - -eB.z;
if( y < mD ){ mD = y; X = gLXnX( llList2Vector( EdgesZ, x ), <0,0,1>, rA ); }
}
if( mD < 0.000001 ) return <-1,-1,-1>;
if( X.x > eB.x ) X.x = eB.x;
else if( X.x < -eB.x ) X.x = -eB.x;
if( X.y > eB.y ) X.y = eB.y;
else if( X.y < -eB.y ) X.y = -eB.y;
if( X.z > eB.z ) X.z = eB.z;
else if( X.z < -eB.z ) X.z = -eB.z;
return Bo + ( X * Br );}
3D
By Nexii Malthus
|
Cylinder and Point, Intersection Boolean | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Finds if there is an intersection of a Point and a Cylinder and returns boolean integer gCXx( vector A, vector O, rotation R, vector S ) {
A = ( A - O ) / R;// Converts to local object frame
return (llPow(A.x/S.x*2,2) + llPow(A.y/S.y*2,2)) <= 1. // Test radius
&& llFabs(A.z/S.z*2) <= 1.;// Test top/bottom
}
3D
By Nexii Malthus
|
Polygon and Point, Intersection Boolean | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Figures out if point is inside of polygon or otherwise. integer gCPXx( list CP, vector X )
{//Copyright (c) 1970-2003, Wm. Randolph Franklin; 2008, Strife Onizuka
integer i = ~(CP != []);
integer c = 0;
if(i < -2){
vector vi = llList2Vector(CP, -1);
do {
vector vj = vi;
vi = llList2Vector(CP, i);
if((vi.y > X.y) ^ (vj.y > X.y)){
if(vj.y != vi.y)
c = c ^ (X.x < (((vj.x - vi.x) * (X.y - vi.y) / (vj.y - vi.y)) + vi.x));
else c = c ^ (0 < ((vj.x-vi.x) * (X.y-vi.y)));
}
} while (++i);
}
return c;
}
2D
Copyright (c) 1970-2003, Wm. Randolph Franklin (Must accept License #1), LSL-Port By Strife Onizuka
|
Polygon and Line Segment, Intersection Boolean | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Figures out if line segment intersects with polygon. integer gVPLSx( vector P0, vector P1, list VP ){
//Copyright 2001, softSurfer (www.softsurfer.com); 2008, Nexii Malthus
if( P0 == P1 ) return gCPXx( VP, P0 );
float tE = 0; float tL = 1;
float t; float N; float D;
vector dS = P1 - P0;
vector e; integer x; integer y = VP!=[];
@start;
for( x = 0; x < y; ++x ){
e = llList2Vector( VP, x+1 ) - llList2Vector( VP, x );
N = Perp( e, P0 - llList2Vector( VP, x ) );
D = -Perp( e, dS );
if( llFabs(D) < 0.00000001 )
if( N < 0 ) return FALSE;
else jump start;
t = N / D;
if( D < 0 ){
if( t > tE ){ tE = t; if( tE > tL ) return FALSE; }
} else {
if( t < tL ){ tL = t; if( tL < tE ) return FALSE; }
} }
// PointOfEntrance = P0 + tE * dS;
// PointOfExit = P0 + tL * dS;
return TRUE;
}
2D
Copyright 2001, softSurfer (www.softsurfer.com) (Must accept License #2), LSL-Port By Nexii Malthus
|
3D Projection | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Projects a vector A by vector B. vector Project3D(vector A,vector B){
return B * ( ( A * B ) / ( B * B ) );}
3D
By Nexii Malthus
|
Reflection | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Reflects Ray R with surface normal N vector Reflect(vector R,vector N){
return R - 2 * N * ( R * N );}
3D
By Nexii Malthus
|
For anyone curious to the shorthand used and who wish to use a lookup table can use this as a reference. Or anyone who wishes to add a new function to the library is welcome to but it would be recommended to keep consistency. I tried to minimize the script function names to be easily readable. All the geometric function names start with a g.
g (Shape1) (Shape2) (Process) (Return (Only needed if other than integer))
Here is the legend:
Shorthand | Name | Description |
---|---|---|
Geometric Types, all the shapes in the library | ||
X | Point | vector defining a point in space |
L | Line | A line has an origin and a direction and is infinitely long |
LS | Line Segment | A line segment is a finite line and therefore consists of a start and end position |
R | Ray | A ray is like a line, except it is more distinct as it defines wether it points forward or back |
P | Plane | A 2D doubly ruled surface of infinite size |
S | Sphere | A sphere is defined by origin and radius (No ellipsoid functions available yet) |
B | Box | A box primitive is six sided and defined by origin, size as well as a rotation. |
C | Cylinder | An elliptic cylinder primitive . |
VP | Convex Polygon | Convex Polygon defined by list of vertices. |
CP | Concave Polygon | Concave Polygon defined by list of vertices. Automatic backward compatibility with Convex Polygons. |
The Process, What does it do? | ||
d | distance | Calculate distance |
n | nearest | Calculate nearest |
p | project | Calculates projection |
x | Intersection | Calculates intersection |
dir | direction | Calculates direction |
Return, What kind of data do I get out of it? | ||
Z | Float | Represents that a float is returned |
V | Vector | Represents that a vector is returned |
O | Origin | Represents the Origin of the ray or line |
D | Direction | Direction from the Origin |
E | Edge | Edge of a shape, such as an edge on a box, suffix may mark special case return type |
#1
//Copyright (c) 1970-2003, Wm. Randolph Franklin
//Copyright (c) 2008, Strife Onizuka (porting to LSL)
//
//Permission is hereby granted, free of charge, to any person obtaining a copy
//of this software and associated documentation files (the "Software"), to deal
//in the Software without restriction, including without limitation the rights
//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
//copies of the Software, and to permit persons to whom the Software is
//furnished to do so, subject to the following conditions:
//
// 1. Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimers.
// 2. Redistributions in binary form must reproduce the above copyright
// notice in the documentation and/or other materials provided with the
// distribution.
// 3. The name of W. Randolph Franklin may not be used to endorse or promote
// products derived from this Software without specific prior written
// permission.
//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
//SOFTWARE.
#2
// Copyright 2001, softSurfer (www.softsurfer.com); 2008, LSL-port by Nexii Malthus
// This code may be freely used and modified for any purpose
// providing that this copyright notice is included with it.
// SoftSurfer makes no warranty for this code, and cannot be held
// liable for any real or imagined damage resulting from its use.
// Users of this code must verify correctness for their application.