Curious about spherical harmonics? This might help! Save this script as a shader and apply it to a high poly sphere at the origin. For bonus points, uncomment the line that uses the color as the vertex position to see the shape of the harmonic.
Feel free to come up with awesome stuff once you’re done.
Shader “Spherical Harmonic” {
Properties {
_SHAr (“First Order Harmonic”, Vector) = (0.0,0.0,0.0,0.0)
_SHAg (“First Order Harmonic”, Vector) = (0.0,0.0,0.0,0.0)
_SHAb (“First Order Harmonic”, Vector) = (0.0,0.0,0.0,0.0)
_SHBr (“Second Order Harmonic”, Vector) = (0.0,0.0,0.0,0.0)
_SHBg (“Second Order Harmonic”, Vector) = (0.0,0.0,0.0,0.0)
_SHBb (“Second Order Harmonic”, Vector) = (0.0,0.0,0.0,0.0)
_SHC (“Third OrderHarmonic”, Vector) = (0.0,0.0,0.0,0.0)
_A (“Alpha”, Float) = 0.5
}
SubShader {
Tags { “Queue”=“Transparent” “IgnoreProjector”=“True” “RenderType”=“Transparent” }
Blend SrcAlpha OneMinusSrcAlpha
Cull Off
Lighting Off
ZWrite On
Pass{
CGPROGRAM
#pragma vertex vert
#pragma fragment frag
#pragma exclude_renderers
#pragma target 2.0
#include “UnityCG.cginc”
#include “Lighting.cginc”
uniform float4 _SHAr;
uniform float4 _SHAg;
uniform float4 _SHAb;
uniform float4 _SHBr;
uniform float4 _SHBg;
uniform float4 _SHBb;
uniform float4 _SHC;
uniform float _A;
struct appdata_t {
float4 vertex : POSITION;
fixed4 color : COLOR;
float3 normal : TEXCOORD0;
float4 tangent : TEXCOORD1;
};
struct v2f {
float4 pos : SV_POSITION;
fixed4 color : COLOR;
};
v2f vert (appdata_t v)
{
v2f o;
UNITY_DIRBASIS;
//This is the spherical harmonic lookup, it takes in the world normal and spits out the appropriate value in that direction
//It comes from appendix 10 of Peter Pike Sloan’s paper “Stupid Spherical Harmonic Tricks”
//It’s a bit more complex than the simpliest transform so it can be more efficient
//http://www.ppsloan.org/publications/StupidSH36.pdf
//It takes 12 coefficients (the numbers in the _SHA,_SHB and _SHC vectors) multiplies them against eachother to construct the harmonic
//Each coefficient represents a cosine wave (which in turn are used to describe the sphere, axis by axis)
//Each level _SHA - _SHB etc divides the sphere into two sub spheres, and each contains more detail (higher frequency data) about the final wave/sphere
//It can be thought of as sound
//Each seperate frequency is a different pitch, and the final sound is all these pieces blended together
float4 wN = v.vertex; //Here I’m using the vertex position since this is for a sphere around the origin
//It’s very similar to a fourier transform, but across the surface of a sphere
half3 x1, x2, x3;
// Linear + constant polynomial terms
x1.r = dot(_SHAr,wN);
x1.g = dot(_SHAg,wN);
x1.b = dot(_SHAb,wN);
// 4 of the quadratic polynomials
half4 vB = wN.xyzz * wN.yzzx;
x2.r = dot(_SHBr,vB);
x2.g = dot(_SHBg,vB);
x2.b = dot(_SHBb,vB);
// Final quadratic polynomial
float vC = wN.xwN.x - wN.ywN.y;
x3 = _SHC.rgb * vC;
float3 shC = x1 + x2 + x3;
//Setup the vertices
o.pos = mul(UNITY_MATRIX_MVP, v.vertex);
//the vectors the rgba colors also work as xyzw in space (color is a space, afterall…)
//i.e. positive and negative red translates verts left and right along the x axis
//o.pos = mul(UNITY_MATRIX_MVP, float4(shC.rgb, 1.0f)); //Comment this in to see the shape of the spherical harmonic
//Set the out color
//o.color = float4(mul(shC, unity_DirBasis), _A); //What was I doing with this?! 
o.color = float4(shC, _A);
return o;
}
fixed4 frag (v2f i) : COLOR
{
float4 c = float4(1.0f,1.0f,1.0f,1.0f);
return i.color;
}
ENDCG
}
}
}
