vec4 v, u;
mat4 m;
v * u component-wise
v * m v is row vector
m * v v is column vector
m * m linear-algebraic matrix multiplication
Inverse 求逆
Transpose 轉置
gl_ModelViewMatrixInverse;
gl_ModelViewProjectionMatrixInverseTranspose
gl_NormalMatrix is the transpose of the inverse of the gl_ModelViewMatrix.
function prototype:
vec4 fract(vec4 x); == x - floor(x); <- [0, 1) // fract 片斷
vec4 clamp(float x, float minVal, float maxVal); returns min(max(x, minVal), maxVal);
vec4 mix(vec4 x, vec4 y, vec4 a); return x * (1.0 - a) + y * a;
vec4 step(vec4 edge, vec4 x); returns 0 if x < edge, otherwise returns 1.
vec4 smoothstep(vec4 edge0, vec4 edge1, vec4 x);
returns if x <= edge0, returns 1 if x >= edge1, perform hermite interpolation
between 0 and 1 when edge0 < x < edge1
０到１之間的Hermite插值算法 equal to
t = clamp((x - edge0) / (edge1 - edge0), 0.0, 1.0);
return t * t * (3 - 2 * t);
vec3 cross(vec3 x, vec3 y); // 只有這種形式，即只有三個component的向量才行 dot(N, L);
result[0] = x[1] * y[2] - x[2] * y[1];
result[1] = x[2] * y[0] - x[0] * y[2];
result[2] = x[0] * y[1] - x[1] * y[0];
float dot(vec4 x, vec4 y);
result = x[0] * y[0] + x[1] * y[1] + ...;
vec4 reflect(vec4 I, vec4 N); // 反射光線向量
For the incident vector I and surface orientation N, returns the reflection direction
result = I - 2.0 * dot(N, I) * N;
vec3 ecPosition = vec3 (gl_ModelViewMatrix * gl_Vertex);
vec3 tnorm = normalize(gl_NormalMatrix * gl_Normal);
vec3 lightVec = normalize(LightPosition - ecPosition);
vec3 reflectVec = reflect(-lightVec, tnorm);
vec3 viewVec = normalize(-ecPosition);
vec4 refract(vec4 I, vec4 N, float eta); // 折射光線向量
For the incident vector I and surface normal N and the ratio(比率) of refraction eta,
returns the refraction vector. The returned result is computed as
k = 1.0 - eta * eta * (1.0 - dot(N, I) * dot(N, I));
if (k < 0.0) {
result = 0.0;
// the return type is float of vec2/3/4
} else {
result = eta * I - (eta * dot(N, I) *sqrt(k)) * N;
}
mat4 matrixComMult(mat4 x, mat4 y); component-wise
to get linear-algebraic multiplication, use the multiply operator (*)
mat4 x, y; x * y;