Difference between revisions of "Interpolation/Linear"

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{{LSL Header|[[Interpolation]]}}
{{RightToc|clear:right;}}


== Linear Interpolation ==
{|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"|
===Float Linear===
|-
|
Linear interpolation of f0 and f1 with fraction t.
<lsl>
float fLin(float f0,float f1,float t) {
    return f0*(1-t) + f1*t;
}
</lsl>
{|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="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
|-
| float f0
| Start (t = 0.0)
|-
| float f1
| End (t = 1.0)
|-
| float t
| Fraction of interpolation
|-
!style="background-color: #d0d0ee" | Output
!style="background-color: #d0d0ee" | Description
|-
| return float fLin
| Returns linear interpolation of two floats
|}
| [[Image:Interp_Chart1.png|center]]
|}
<div style="float:right;font-size: 80%;">
Released to Public Domain. By Nexii Malthus</div>
|}
{|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"|
===Vector Linear===
|-
|
Linear interpolation of v0 and v1 with fraction t.
<lsl>
vector vLin(vector v0, vector v1,float t){
    return v0*(1-t) + v1*t;
}
</lsl>
{|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="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 v0
| Start (t = 0.0)
|-
| vector v1
| End (t = 1.0)
|-
| float t
| Fraction of interpolation
|-
!style="background-color: #d0d0ee" | Output
!style="background-color: #d0d0ee" | Description
|-
| return vector vLin
| Returns linear interpolation of two vectors
|}
| Graph goes here, k.
|}
<div style="float:right;font-size: 80%;">
Released to Public Domain. By Nexii Malthus</div>
|}
{|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"|
===Rotation Linear===
|-
|
Spherical Linear interpolation of r0 and r1 with fraction t.
Also known as '''SLERP'''
<lsl>
rotation rLin(rotation r0,rotation r1,float t) {
    float ang = llAngleBetween(r0, r1);
    if(ang > PI) ang -= TWO_PI;
    return r0 * llAxisAngle2Rot( llRot2Axis(r1/r0)*r0, ang*t);
}
</lsl>
{|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="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
|-
| rotation r0
| Start (t = 0.0)
|-
| rotation r1
| End (t = 1.0)
|-
| float t
| Fraction of interpolation
|-
!style="background-color: #d0d0ee" | Output
!style="background-color: #d0d0ee" | Description
|-
| return rotation rLin
| Returns spherical linear interpolation of two rotations
|}
| Graph goes here, k.
|}
<div style="float:right;font-size: 80%;">
Released to Public Domain. By Nexii Malthus</div>
|}
{|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"|
===Vector List, Linear===
|-
|
Interpolates between two vectors in a list of vectors.
<lsl>
vector pLin(list v, float t, integer Loop ){
  float l = llGetListLength(v); t *= l-1;
  float f = (float)llFloor(t);
  integer i1 = 0; integer i2 = 0;
  if(Loop){ i1 = (integer)(f-llFloor(f/l)*l);
        ++f;i2 = (integer)(f-llFloor(f/l)*l);}
  else {
    if(  f > l-1 ) i1 = (integer)l-1;
    else if(  f >= 0 ) i1 = (integer)f;
    if(f+1 > l-1 ) i2 = (integer)l-1;
    else if(f+1 >= 0 ) i2 = (integer)f+1; }
  vector v1 = llList2Vector(v, i1);
  vector v2 = llList2Vector(v, i2);
  return vLin( v1, v2, t-f );}
</lsl>
{|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="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 v
| A path of vectors.
|-
| float t
| Interpolation, Start 0.0 - 1.0 End.
|-
| integer Loop
| Whether the list loops over.
|-
!style="background-color: #d0d0ee" | Output
!style="background-color: #d0d0ee" | Description
|-
| return vector pLin
| Returns a vector that is the linear interpolation of two vectors between 't'.
|}
| Graph goes here, k.
|}
<div style="float:right;font-size: 80%;">
Released to Public Domain. By Nexii Malthus</div>
|}

Latest revision as of 03:37, 14 September 2011

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