1.阈值函数，float step(float edge, float x)

x<edge是0，大于等于是1。经常用来代替if

float edge = 0.5; float x = 0.3; float result = step(edge, x); // will return 0.0 since `x` < `edge`

2.光滑阈值函数，smoothInterpolation = smoothstep(edge0, edge1, x)

x<edge0是0，>edge1是1，中间是0-1光滑曲线。

// result will be a smooth color interpolation between red and blue vec3 out = mix(color1, color2, smoothstep(0.2, 0.8, factor));

3.绝对值函数，float abs(float x);

float number = -5.0; float absValue = abs(number); // will be 5.0

4.向上取整，ceil()

float number = 3.5; float ceilVal = ceil(number); // will be 4.0 vec3 vector = vec3(2.3, 5.8, -4.7); vec3 ceilVec = ceil(vector); // will be vec3(3.0, 6.0, -4.0)

5.向下取整，floor()

float val = 3.7; float flooredVal = floor(val); // will be 3.0 float val = -3.7; float flooredVal = floor(val); // will be -4.0

6.截断成整数，int()

float floatVal = 3.7; int intVal = int(floatVal); // will be 3

7.取小数部分，fract()

float val = 3.7; float fractVal = fract(val); //fractVal=0.7

8.计算向量长度，length()

vec3 vec = vec3(2.0, 4.0, 4.0); float vecLength = length(vec); // will be 6.0

9.计算向量距离，float distance(vec p0, vec p1)

vec3 p0 = vec3(1.0, 2.0, 2.0); vec3 p1 = vec3(4.0, 2.0, 6.0); float dist = distance(p0, p1); // will be 5.0

10.计算与x轴正方向夹角，float atan(float y, float x)

float dx = targetX - positionX; float dy = targetY - positionY; float angle = atan(dy, dx); // Calculate angle for rotation

11.sin周期函数，float sin(float angle)

float angle = uv.x * 2.0 * PI; //一个周期 float angle = uv.x * frequency * 2.0 * PI; //frequency 个周期

12.向量归一化函数，normalize(V)

N = normalize(V);

向量归一化后，取normalize.x就是向量和x正方向夹角的cos值，normalize.y就是向量和y正方向夹角的sin值。

13.点乘，可以是两个float，也可以是两个向量，float dot(float x, float y)；float dot(vec2 x, vec2 y)

代数意义：v1 * v2 = v1[0] * v2[0] + … + v1[n] * v2[n];

几何意义：①：非归一化向量dot表示cos值乘上两个向量的长度
v1 * v2 = length(v1) * length(v2) * cos(angle between v1 and v2)

②：归一化向量dot表示cos值：

v1 * v2 = cos(angle between v1 and v2);

14.上限和下限值限制函数clamp，float clamp(float value, float minVal, float maxVal)：

超过maxVal部分都等于maxVal，小于minVal部分都等于minVal

clamp(0.8, 0.0, 1.0); // will be 0.8, since value is between 0.0 and 1.0 clamp(-0.5, 0.0, 1.0); // will be 0.0, since value is less than 0.0 clamp(1.5, 0.0, 1.0); // will be 1.0, since value is greater than 1.0

15.纹理采样函数，vec4 color = texture(<Name>, texCoord);

uniform sampler2D <Name> vec4 color = texture(<Name>, texCoord);

16.线性插值函数，T mix(T start, T end, T t)

注意start是1-t：mix(start, end, t) = start * (1 - t) + end * t

vec3 color1 = vec3(1.0, 0.0, 0.0); // red color vec3 color2 = vec3(0.0, 0.0, 1.0); // blue color float factor = 0.5; // interpolation factor // result will be a purple color (halfway between red and blue) vec3 resultColor = mix(color1, color2, factor);

17.取余。float mod(float x, float y);

float result = mod(10.0, 3.0); // Result will be 1.0 (10 / 3 has a remainder of 1) float result = mod(-10.0, 3.0); // Result will be 2.0 (-10 / 3 has a remainder of 2)

18.计算反正切值。atan(y, x)函数用于计算(x, y)二维笛卡尔坐标系中某一点与正x 轴之间的弧度角

float dx = targetX - positionX; float dy = targetY - positionY; float angle = atan(dy, dx); // Calculate angle for rotation