Unity&Shader基础篇-常用函数的使用与案例

一、前言

继前面的系列文章之后，本篇继续讲解Cg的常用函数的使用案例，帮助巩固Cg语言的基础知识。这些函数都可以在Cg的教程里The Cg Tutorial找到示例代码和函数意义。本文讲解几个常用的函数，分别有

1、Step(a,x):如果x<a返回0；如果x>或=a返回1

2、Clamp(x,a,a):如果x<a返回a；如果x>b返回b；如果在a和b之间就返回x

3、smoothstep(min,max,x):返回的值为–2*(( x – min )/( max – min ))³ +3*(( x – min )/( max – min ))²

4、lerp(a,b,f):线性插值函数，返回值为（1-f）*a+b*f

5、三角函数sin、cos

二、常用函数的使用实例

1、Step函数：在Unity中的Shader代码

Shader "Unlit/Chapter5-Step"
{
Properties
{
_background("背景色",Color)=(0,0,0,0)
}
SubShader
{
// No culling or depth
Cull Off ZWrite Off ZTest Always

CGINCLUDE
ENDCG


Pass
{
CGPROGRAM
#pragma vertex vert
#pragma fragment frag

#include "UnityCG.cginc"
float4 _background;

struct appdata
{
float4 vertex : POSITION;
float2 uv : TEXCOORD0;
};

struct v2f
{
float2 uv : TEXCOORD0;
float4 vertex : SV_POSITION;
};

v2f vert(appdata v)
{
v2f o;
o.vertex = mul(UNITY_MATRIX_MVP, v.vertex);
o.uv = v.uv;
o.uv.y = 1 - o.uv.y;
return o;
}

// Functions
fixed4 frag(v2f i) : SV_Target
{
float2 r = 2.0*(i.uv - 0.5);
//_ScreenParams是Unity内置的变量
float aspectRatio = _ScreenParams.x / _ScreenParams.y;
r.x *= aspectRatio;

fixed3 pixel = _background.xyz;
float edge, variable, ret;

//将屏幕划分成五个部分

//第一部分
if (r.x < -0.6*aspectRatio)
{
variable = r.y;
edge = 0.2;
if (variable > edge)
{
ret = 1.0;
}
else
{
ret = 0;
}
}
else if (r.x < -0.2*aspectRatio)
{
variable = r.y;
edge = -0.2;
//step(a,x):如果x<a结果返回0，反之返回1
ret = step(edge, variable);
}
else if (r.x < 0.2*aspectRatio)
{
ret = 1.0 - step(0.5, r.y);
}
else if (r.x < 0.6*aspectRatio)
{
ret = 0.3 + 0.5*step(-0.4, r.y);
}
else
{
ret = step(-0.3, r.y) * (1.0 - step(0.2, r.y));
}
pixel = fixed3(ret, ret, ret);
return fixed4(pixel, 1.0);

}


ENDCG
}
}
}

得到的效果图如图所示：
2、Clamp：在Unity中的代码如下：

Shader "Unlit/Chapter5-Clamp"
{
Properties
{
_background("背景色",Color) = (0,0,0,0)
}
SubShader
{
// No culling or depth
Cull Off ZWrite Off ZTest Always

// 追加
CGINCLUDE
//定义宏
#define PI 3.14159
ENDCG


Pass
{
CGPROGRAM
#pragma vertex vert
#pragma fragment frag

#include "UnityCG.cginc"

float4 _background;

struct appdata
{
float4 vertex : POSITION;
float2 uv : TEXCOORD0;
};

struct v2f
{
float2 uv : TEXCOORD0;
float4 vertex : SV_POSITION;
};

v2f vert(appdata v)
{
v2f o;
o.vertex = mul(UNITY_MATRIX_MVP, v.vertex);
o.uv = v.uv;
o.uv.y = 1 - o.uv.y;
return o;
}

// Functions
fixed4 frag(v2f i) : SV_Target
{
float2 r = 2.0*(i.uv - 0.5);
//_ScreenParams是Unity内置的变量
float aspectRatio = _ScreenParams.x / _ScreenParams.y;
r.x *= aspectRatio;

fixed3 pixel = _background.xyz;
float edge, variable, ret;

//第一部分
if (i.uv.x < 0.25) { // part1
ret = i.uv.y;
}
else if (i.uv.x < 0.5) { // part2
float minVal = 0.3;
float maxVal = 0.6;
variable = i.uv.y;
if (variable < minVal) {
ret = minVal;
}
if (variable > minVal && variable < maxVal) {
ret = variable;
}
if (variable > maxVal) {
ret = maxVal;
}
}
else if (i.uv.x < 0.75) { // part3
float minVal = 0.6;
float maxVal = 0.8;
variable = i.uv.y;
//clam(x,a,b)：x如果小于a返回a，如果大于b返回b，在a~b范围内返回x
ret = clamp(variable, minVal, maxVal);
}
else { // part4
float y = cos(5.0 * 2.0 * PI *i.uv.y);
y = (y + 1.0)*0.5; // map [-1,1] to [0,1]
ret = clamp(y, 0.2, 0.8);
}

pixel = fixed3(ret, ret, ret);
return fixed4(pixel, 1.0);

}


ENDCG
}
}
}

效果图如图所示：
说明：对比1和2的图会明显发现，在使用Clamp处理的时候，边缘的颜色会有渐变的效果。3、smoothstep：这个脚本只给出片段着色器部分，其他部分同2，代码如下：

fixed4 frag(v2f i) : SV_Target
{

fixed3 pixel = _background.xyz;

float edge, variable, ret;

if (i.uv.x < 1.0 / 5.0) { // part1
edge = 0.5;
ret = step(edge, i.uv.y);
}
else if (i.uv.x < 2.0 / 5.0) { // part2
float edge0 = 0.45;
float edge1 = 0.55;
float t = (i.uv.y - edge0) / (edge1 - edge0);
float t1 = clamp(t, 0.0, 1.0);
ret = t1;
}
else if (i.uv.x < 3.0 / 5.0) { // part3
float edge0 = 0.45;
float edge1 = 0.55;
float t = clamp((i.uv.y - edge0) / (edge1 - edge0), 0.0, 1.0);
float t1 = 3.0*t*t - 2.0*t*t*t;
ret = t1;
}
else if (i.uv.x < 4.0 / 5.0) { // part4

//smoothstep(min,max,x)：x=-2*((x-min)/(max-min))^3+3*((x-min)/(max-min))^2，当x=min时返回0，当x=max时返回1
ret = smoothstep(0.45, 0.55, i.uv.y);
}
else if (i.uv.x < 5.0 / 5.0) {
float edge0 = 0.45;
float edge1 = 0.55;
float t = clamp((i.uv.y - edge0) / (edge1 - edge0), 0.0, 1.0);
float t1 = t*t*t*(t*(t*6.0 - 15.0) + 10.0);
ret = t1;
}


pixel = fixed3(ret, ret, ret);
return fixed4(pixel, 1.0);
}

得到的效果图如上图所示，这个效果要对比之前的两个，可以发现有明显的过渡效果。当然不是说这个函数就比之前的函数好用，各有千秋，只是在本篇文章中特有的安排而已。4、lerp函数，Unity中的Shader代码如下：

Shader "Unlit/Chapter5-Lerp"
{
Properties
{
_background("背景色",Color) = (0,0,0,0)
_col1("颜色1",Color)=(0,0,0,0)
_col2("颜色2",Color)=(0,0,0,0)
}
SubShader
{
// No culling or depth
Cull Off ZWrite Off ZTest Always

CGINCLUDE
//定义宏
#define PI 3.14159
ENDCG


Pass
{
CGPROGRAM
#pragma vertex vert
#pragma fragment frag

#include "UnityCG.cginc"

float4 _background;
float4 _col1;
float4 _col2;

struct appdata
{
float4 vertex : POSITION;
float2 uv : TEXCOORD0;
};

struct v2f
{
float2 uv : TEXCOORD0;
float4 vertex : SV_POSITION;
};

v2f vert(appdata v)
{
v2f o;
o.vertex = mul(UNITY_MATRIX_MVP, v.vertex);
o.uv = v.uv;
o.uv.y = 1 - o.uv.y;
return o;
}
// Functions
fixed4 frag(v2f i) : SV_Target
{

fixed3 pixel = _background.xyz;

fixed3 ret;

if (i.uv.x < 1.0 / 5.0) { // part1
float x0 = 0.2;
float x1 = 0.7;
float m = 0.1;
float val = x0 * (1.0 - m) + x1*m;
ret = fixed3(val, val, val);
}
else if (i.uv.x < 2.0 / 5.0) { // part2
float x0 = 0.2;
float x1 = 0.7;
float m = i.uv.y;
float val = x0*(1.0 - m) + x1*m;
ret = fixed3(val, val, val);
}
else if (i.uv.x < 3.0 / 5.0) { // part3
float x0 = 0.2;
float x1 = 0.7;
float m = i.uv.y;
//lerp(a,b,f)返回(1-f)*a+b*f
float val = lerp(x0, x1, m);
ret = fixed3(val, val, val);

}
else if (i.uv.x < 4.0 / 5.0) { // part4
float m = i.uv.y;
ret = lerp(_col1, _col2, m);
}
else if (i.uv.x < 5.0 / 5.0) {
float m = smoothstep(0.5, 0.6, i.uv.y);
ret = lerp(_col1, _col2, m);
}
pixel = ret;
return fixed4(pixel, 1.0);
}


ENDCG
}
}
}

效果图如图所示：这个Shader中对lerp函数和smoothstep函数做了对比，其中第三个区域是使用lerp函数的效果，第四个区域是先进行了smoothstep处理在进行lerp处理的效果。5、lerp函数与直接的颜色加减进行对比：完整的Shader代码如下：

Shader "Unlit/Chapter5-ColorAdd&Substr"
{
Properties
{

}
SubShader
{
// No culling or depth
Cull Off ZWrite Off ZTest Always

// 追加
CGINCLUDE
// 添加画圆盘的方法
float disk(float2 r, float2 center, float radius) {
float distanceFromCenter = length(r - center);
float outsideOfDisk = smoothstep(radius - 0.005, radius + 0.005, distanceFromCenter);
float insideOfDisk = 1.0 - outsideOfDisk;
return insideOfDisk;

}
ENDCG


Pass
{
CGPROGRAM
#pragma vertex vert
#pragma fragment frag

#include "UnityCG.cginc"

struct appdata
{
float4 vertex : POSITION;
float2 uv : TEXCOORD0;
};

struct v2f
{
float2 uv : TEXCOORD0;
float4 vertex : SV_POSITION;
};

v2f vert(appdata v)
{
v2f o;
o.vertex = mul(UNITY_MATRIX_MVP, v.vertex);
o.uv = v.uv;
o.uv.y = 1 - o.uv.y;
return o;
}

// ANTI-ALIASING WITH SMOOTHSTEP
fixed4 frag(v2f i) : SV_Target
{
float2 r = 2.0 * (i.uv - 0.5);
float aspectRatio = _ScreenParams.x / _ScreenParams.y;
r.x *= aspectRatio;

fixed3 black = float3(0.0, 0.0, 0.0); // black
fixed3 white = float3(1.0, 1.0, 1.0);
fixed3 gray = float3(0.3, 0.3, 0.3);
fixed3 col1 = float3(0.216, 0.471, 0.698); // blue
fixed3 col2 = float3(1.00, 0.329, 0.298); // red
fixed3 col3 = float3(0.867, 0.910, 0.247); // yellow

fixed3 ret;
fixed3 pixel;
float d;


//三个部分的画法各有优势

//第一部分背景是灰色，简单的覆盖叠加
if (i.uv.x < 1.0 / 3.0) { // part1
ret = gray;
d = disk(r, float2(-1.1, 0.3), 0.4);
ret = lerp(ret, col1, d);
d = disk(r, float2(-1.3, 0.0), 0.4);
ret = lerp(ret, col2, d);
d = disk(r, float2(-1.05, -0.3), 0.4);
ret = lerp(ret, col3, d);
}

//第二部分背景是黑色，通过颜色相加来实现
else if (i.uv.x < 2.0 / 3.0) { // part2
   // Color addition
ret = black;
ret += disk(r, float2(0.1, 0.3), 0.4) * col1;
ret += disk(r, float2(-0.1, 0.0), 0.4) * col2;
ret += disk(r, float2(0.15, -0.3), 0.4) * col3;
}

//第三部分背景是白色，通过相减来实现颜色的显示
else if (i.uv.x < 3.0 / 3.0) { // part3
   // Color substraction
ret = white;
ret -= disk(r, float2(1.1, 0.3), 0.4) * col1;
ret -= disk(r, float2(1.05, 0.0), 0.4) * col2;
ret -= disk(r, float2(1.35, -0.25), 0.4) * col3;

}
pixel = ret;
return fixed4(pixel, 1.0);
}


ENDCG
}
}
}

得到的效果图如图所示：第一部分通过lerp函数来处理颜色重叠的部分，第二、三部分之间通过颜色的加减来处理颜色重叠的部分。
6、三角函数，sin、cos函数：利用正弦余弦函数来做图形的旋转，效果图如图所示：
蓝色的网格和蓝色的矩形、圆盘都是固定的，旋转的是红色的网格以及网格上的矩阵和圆盘，它的shader代码如下：

Shader "Unlit/Chapter6-Rotation"
{
Properties
{
_RotateAngle("旋转的角度",Range(0,360))=36
}
SubShader
{
// No culling or depth
Cull Off ZWrite Off ZTest Always

// 
CGINCLUDE

#define PI 3.14159

// 使用函数来创建网格，返回的值再乘以颜色及得到网格图形
float coordinateGrid(float2 r) 
{
float3 axisCol = float3(0.0, 0.0, 1.0);
float3 gridCol = float3(0.5, 0.5, 0.5);
float ret = 0.0;

// 画线
const float tickWidth = 0.1;
for (float i = -2.0; i<2.0; i += tickWidth) {
ret += 1.0 - smoothstep(0.0, 0.008, abs(r.x - i));
ret += 1.0 - smoothstep(0.0, 0.008, abs(r.y - i));
}

// 画坐标轴
ret += 1.0 - smoothstep(0.001, 0.015, abs(r.x));
ret += 1.0 - smoothstep(0.001, 0.015, abs(r.y));
return ret;
}

// 在圆盘里面的都返回1
float disk(float2 r, float2 center, float radius) {
return 1.0 - smoothstep(radius - 0.005, radius + 0.005, length(r - center));
}

// 在长方形里面的都返回1
float rectangle(float2 r, float2 bottomLeft, float2 topRight) {
float ret;
float d = 0.005;
ret = smoothstep(bottomLeft.x - d, bottomLeft.x + d, r.x);
ret *= smoothstep(bottomLeft.y - d, bottomLeft.y + d, r.y);
ret *= 1.0 - smoothstep(topRight.y - d, topRight.y + d, r.y);
ret *= 1.0 - smoothstep(topRight.x - d, topRight.x + d, r.x);
return ret;
}
ENDCG


Pass
{
CGPROGRAM
#pragma vertex vert
#pragma fragment frag

#include "UnityCG.cginc"

uniform float _RotateAngle;

struct appdata
{
float4 vertex : POSITION;
float2 uv : TEXCOORD0;
};

struct v2f
{
float2 uv : TEXCOORD0;
float4 vertex : SV_POSITION;
};

v2f vert(appdata v)
{
v2f o;
o.vertex = mul(UNITY_MATRIX_MVP, v.vertex);
o.uv = v.uv;
o.uv.y = 1 - o.uv.y;
return o;
}

//坐标变换：旋转
fixed4 frag(v2f i) : SV_Target
{
float2 r = 2.0 * (i.uv - 0.5);
float aspectRatio = _ScreenParams.x / _ScreenParams.y;
r.x *= aspectRatio;

fixed3 bgCol = float3(1.0, 1.0, 1.0); // white

fixed3 col1 = float3(0.216, 0.471, 0.698); // blue
fixed3 col2 = float3(1.00, 0.329, 0.298); // red
fixed3 col3 = float3(0.867, 0.910, 0.247); // yellow

fixed3 ret;
float2 q;
float angle;
//angle = 0.2*PI; // 旋转36度
angle = _RotateAngle / PI;
q.x = cos(angle)*r.x + sin(angle)*r.y;
q.y = -sin(angle)*r.x + cos(angle)*r.y;

ret = bgCol;
// 画出这两个坐标系

//底色浅一点为固定轴
ret = lerp(ret, col1, coordinateGrid(r)*0.4);

//要旋转的坐标轴
ret = lerp(ret, col2, coordinateGrid(q));

// 画出各种图形

//在固定坐标系的图形
ret = lerp(ret, col1, disk(r, float2(1.0, 0.0), 0.2));
ret = lerp(ret, col1, rectangle(r, float2(-0.8, 0.2), float2(-0.5, 0.4)));

//在可旋转坐标系的图形
ret = lerp(ret, col2, disk(q, float2(1.0, 0.0), 0.2));
ret = lerp(ret, col2, rectangle(q, float2(-0.8, 0.2),float2(-0.5, 0.4)));

fixed3 pixel = ret;
return fixed4(pixel, 1.0);
}


ENDCG
}
}
}

7、使用lerp函数来进行缩放，效果图所示：同样，蓝色部分是固定的，红色部分是缩放的的对象。
缩放的Shader的代码如下：

Shader "Unlit/Chapter6-Scale"
{
Properties
{
_ScaleValue("缩放因子",Range(0.1,10))=1
}
SubShader
{
// No culling or depth
Cull Off ZWrite Off ZTest Always

CGINCLUDE

#define PI 3.14159

// 使用函数来创建网格，返回的值再乘以颜色及得到网格图形
float coordinateGrid(float2 r) {
float3 axisCol = float3(0.0, 0.0, 1.0);
float3 gridCol = float3(0.5, 0.5, 0.5);
float ret = 0.0;

// 画网格
const float tickWidth = 0.1;
for (float i = -2.0; i<2.0; i += tickWidth) {
ret += 1.0 - smoothstep(0.0, 0.008, abs(r.x - i));
ret += 1.0 - smoothstep(0.0, 0.008, abs(r.y - i));
}

// 画坐标轴
ret += 1.0 - smoothstep(0.001, 0.015, abs(r.x));
ret += 1.0 - smoothstep(0.001, 0.015, abs(r.y));
return ret;
}

// 在圆盘内的返回1
float disk(float2 r, float2 center, float radius) {
return 1.0 - smoothstep(radius - 0.005, radius + 0.005, length(r - center));
}

// 在长方形内的返回1
float rectangle(float2 r, float2 bottomLeft, float2 topRight) {
float ret;
float d = 0.005;
ret = smoothstep(bottomLeft.x - d, bottomLeft.x + d, r.x);
ret *= smoothstep(bottomLeft.y - d, bottomLeft.y + d, r.y);
ret *= 1.0 - smoothstep(topRight.y - d, topRight.y + d, r.y);
ret *= 1.0 - smoothstep(topRight.x - d, topRight.x + d, r.x);
return ret;
}
ENDCG


Pass
{
CGPROGRAM
#pragma vertex vert
#pragma fragment frag

#include "UnityCG.cginc"

uniform float _ScaleValue;

struct appdata
{
float4 vertex : POSITION;
float2 uv : TEXCOORD0;
};

struct v2f
{
float2 uv : TEXCOORD0;
float4 vertex : SV_POSITION;
};

v2f vert(appdata v)
{
v2f o;
o.vertex = mul(UNITY_MATRIX_MVP, v.vertex);
o.uv = v.uv;
o.uv.y = 1 - o.uv.y;
return o;
}

//坐标转换：缩放
fixed4 frag(v2f i) : SV_Target
{
float2 r = 2.0 * (i.uv - 0.5);
float aspectRatio = _ScreenParams.x / _ScreenParams.y;
r.x *= aspectRatio;

fixed3 bgCol = float3(1.0, 1.0, 1.0); // white

fixed3 col1 = float3(0.216, 0.471, 0.698); // blue
fixed3 col2 = float3(1.00, 0.329, 0.298); // red
fixed3 col3 = float3(0.867, 0.910, 0.247); // yellow

fixed3 ret;
ret = bgCol;

// 固定的坐标系
ret = lerp(ret, col1, coordinateGrid(r) / 2.0);

// 缩放
float2 q = _ScaleValue*r;
ret = lerp(ret, col2, coordinateGrid(q));

// 画各个图形

//在原始坐标系中画
ret = lerp(ret, col1, disk(r, float2(0.0, 0.0), 0.1));
ret = lerp(ret, col1, rectangle(r, float2(-0.5, 0.0),float2(-0.2, 0.2)));

//在可缩放坐标系中画
ret = lerp(ret, col2, disk(q, float2(0.0, 0.0), 0.1)); //大
ret = lerp(ret, col2, rectangle(q, float2(-0.5, 0.0),float2(-0.2, 0.2))); //大



fixed3 pixel = ret;
return fixed4(pixel, 1.0);
}


ENDCG
}
}
}

8、平移以及旋转和平移的组合，效果如图所示，这个Shader部分分了两个部分对旋转和平移进行组合使用，分别是
先旋转在平移和先平移再旋转，Shader的代码如下：

Shader "Unlit/Chapter6-Transform"
{
Properties
{
_RotationAngle("旋转角",Range(0,360))=0
_LRotatedTranslatedX("左半部分X方向平移",Range(0,1))=0
_LRotatedTranslatedY("左半部分Y方向平移",Range(0,1))=0

_RRotatedTranslatedX("右半部分X方向平移",Range(0,1)) = 0
_RRotatedTranslatedY("右半部分Y方向平移",Range(0,1)) = 0
}
SubShader
{
// No culling or depth
Cull Off ZWrite Off ZTest Always
CGINCLUDE
#define PI 3.1415926

// 通过函数来画网格
float coordinateGrid(float2 r) {
float3 axisCol = float3(0.0, 0.0, 1.0);
float3 gridCol = float3(0.5, 0.5, 0.5);
float ret = 0.0;

// 画网线
const float tickWidth = 0.1;
for (float i = -2.0; i<2.0; i += tickWidth) {
ret += 1.0 - smoothstep(0.0, 0.008, abs(r.x - i));
ret += 1.0 - smoothstep(0.0, 0.008, abs(r.y - i));
}

// 画坐标轴
ret += 1.0 - smoothstep(0.001, 0.015, abs(r.x));
ret += 1.0 - smoothstep(0.001, 0.015, abs(r.y));
return ret;
}

// 圆内的返回1
float disk(float2 r, float2 center, float radius) {
return 1.0 - smoothstep(radius - 0.005, radius + 0.005, length(r - center));
}

// 在长方形内返回1
float rectangle(float2 r, float2 bottomLeft, float2 topRight) {
float ret;
float d = 0.005;
ret = smoothstep(bottomLeft.x - d, bottomLeft.x + d, r.x);
ret *= smoothstep(bottomLeft.y - d, bottomLeft.y + d, r.y);
ret *= 1.0 - smoothstep(topRight.y - d, topRight.y + d, r.y);
ret *= 1.0 - smoothstep(topRight.x - d, topRight.x + d, r.x);
return ret;
}
ENDCG


Pass
{
CGPROGRAM
#pragma vertex vert
#pragma fragment frag

#include "UnityCG.cginc"

uniform float _RotationAngle;
uniform float _LRotatedTranslatedX;
uniform float _LRotatedTranslatedY;
uniform float _RRotatedTranslatedX;
uniform float _RRotatedTranslatedY;


struct appdata
{
float4 vertex : POSITION;
float2 uv : TEXCOORD0;
};

struct v2f
{
float2 uv : TEXCOORD0;
float4 vertex : SV_POSITION;
};

v2f vert(appdata v)
{
v2f o;
o.vertex = mul(UNITY_MATRIX_MVP, v.vertex);
o.uv = v.uv;
o.uv.y = 1 - o.uv.y;
return o;
}

//坐标旋转和平移
fixed4 frag(v2f i) : SV_Target
{
float2 r = 2.0 * (i.uv - 0.5);
float aspectRatio = _ScreenParams.x / _ScreenParams.y;
r.x *= aspectRatio;

fixed3 bgCol = float3(1.0, 1.0, 1.0); // white

fixed3 col1 = float3(0.216, 0.471, 0.698); // blue
fixed3 col2 = float3(1.00, 0.329, 0.298); // red
fixed3 col3 = float3(0.867, 0.910, 0.247); // yellow

fixed3 ret;
ret = bgCol;

float angle = _RotationAngle/PI;
float2x2 rotationMatrix = float2x2(cos(angle), -sin(angle),
sin(angle), cos(angle));

//分两部分进行转换

//左半部分
if (i.uv.x < 1.0 / 2.0) 
{
r = r - float2(-aspectRatio / 2.0, 0);
float2 rotated = mul(rotationMatrix, r);
float2 rotatedTranslated = rotated - float2(_LRotatedTranslatedX, _LRotatedTranslatedY);

//原始坐标
ret = lerp(ret, col1, coordinateGrid(r) * 0.3);
//旋转坐标
ret = lerp(ret, col2, coordinateGrid(rotated)*0.3);
//旋转再平移
ret = lerp(ret, col3, coordinateGrid(rotatedTranslated)*0.3);

//原始坐标的图形
ret = lerp(ret, col1, rectangle(r, float2(-0.1, -0.2), float2(0.1, 0.2)));
//旋转之后的坐标图形
ret = lerp(ret, col2, rectangle(rotated, float2(-0.1, -0.2), float2(0.1, 0.2)));
//旋转再平移之后
ret = lerp(ret, col3, rectangle(rotatedTranslated, float2(-0.1, -0.2), float2(0.1, 0.2)));
}

//右半部分
else if (i.uv.x < 2.0 / 2.0) { 

r = r - float2(aspectRatio / 2.0, 0);
//平移
float2 translated = r - float2(_RRotatedTranslatedX, _RRotatedTranslatedY);
//平移再旋转
float2 translatedRotated = mul(rotationMatrix, translated);

//原始坐标
ret = lerp(ret, col1, coordinateGrid(r) * 0.3);
//平移
ret = lerp(ret, col2, coordinateGrid(translated)*0.3);
//平移之后再旋转
ret = lerp(ret, col3, coordinateGrid(translatedRotated)*0.3);

ret = lerp(ret, col1, rectangle(r, float2(-0.1, -0.2), float2(0.1, 0.2)));
ret = lerp(ret, col2, rectangle(translated, float2(-0.1, -0.2), float2(0.1, 0.2)));
ret = lerp(ret, col3, rectangle(translatedRotated, float2(-0.1, -0.2), float2(0.1, 0.2)));
}




fixed3 pixel = ret;
return fixed4(pixel, 1.0);
}


ENDCG
}
}
}

三、放两个大招—各种动画效果

1、效果如图所示：从左到右分别是五个不同的动画效果，使用到的函数都是前面讲解的函数加上之后补充的旋转、缩放和平移效果。

Shader代码如下：（原文地址凯尔八阿哥专栏，转载请注明出处）

Shader "Unlit/Chapter6-Animations"
{
Properties
{
_SpeedY("第一部分的速度",Range(0,3)) = 1
_Amplitude("第二部分的振幅",Range(0,1)) = 0.8
_RSpeedX("圆周运动X方向的速度",Range(0,10)) = 5
_RSpeedY("圆周运动Y方向的速度",Range(0,10)) = 5
_RAmplitudeY("圆周运动Y方向的幅度",Range(0,1)) = 0.1
_RAmplitudeX("圆周运动X方向的幅度",Range(0,1)) = 0.1
_ChainAnimSpeed("链条运动的速度",Range(0,10)) = 5
_ChainAnimRotaSpeed("链条运动的旋转速度",Range(0,10)) = 3
_JumpSpeed("跳跃运动的速度",Range(0,10))=2

}
SubShader
{
// No culling or depth
Cull Off ZWrite Off ZTest Always
CGINCLUDE
#define PI 3.1415926

// 通过函数来画网格
float coordinateGrid(float2 r) {
float3 axisCol = float3(0.0, 0.0, 1.0);
float3 gridCol = float3(0.5, 0.5, 0.5);
float ret = 0.0;

// 画网线
const float tickWidth = 0.1;
for (float i = -2.0; i<2.0; i += tickWidth) {
ret += 1.0 - smoothstep(0.0, 0.008, abs(r.x - i));
ret += 1.0 - smoothstep(0.0, 0.008, abs(r.y - i));
}

// 画坐标轴
ret += 1.0 - smoothstep(0.001, 0.015, abs(r.x));
ret += 1.0 - smoothstep(0.001, 0.015, abs(r.y));
return ret;
}

// 圆内的返回1
float disk(float2 r, float2 center, float radius) 
{
return 1.0 - smoothstep(radius - 0.005, radius + 0.005, length(r - center));
}

// 在长方形内返回1
float rectangle(float2 r, float2 bottomLeft, float2 topRight) 
{
float ret;
float d = 0.005;
ret = smoothstep(bottomLeft.x - d, bottomLeft.x + d, r.x);
ret *= smoothstep(bottomLeft.y - d, bottomLeft.y + d, r.y);
ret *= 1.0 - smoothstep(topRight.y - d, topRight.y + d, r.y);
ret *= 1.0 - smoothstep(topRight.x - d, topRight.x + d, r.x);
return ret;
}
float mod(float  a, float  b) 
{ 
return a - b*floor(a / b); 
}
ENDCG


Pass
{
CGPROGRAM
#pragma vertex vert
#pragma fragment frag

#include "UnityCG.cginc"
uniform float _Amplitude;
uniform float _SpeedY;
uniform float _RSpeedX;
uniform float _RSpeedY;
uniform float _RAmplitudeY;
uniform float _RAmplitudeX;
uniform float _ChainAnimSpeed;
uniform float _ChainAnimRotaSpeed;
uniform float _JumpSpeed;

struct appdata
{
float4 vertex : POSITION;
float2 uv : TEXCOORD0;
};

struct v2f
{
float2 uv : TEXCOORD0;
float4 vertex : SV_POSITION;
};

v2f vert(appdata v)
{
v2f o;
o.vertex = mul(UNITY_MATRIX_MVP, v.vertex);
o.uv = v.uv;
o.uv.y = 1 - o.uv.y;
return o;
}

//动画，使用到了Unity内置的变量_Time 四维向量(t/20, t, t*2, t*3)，_Time.y=t;
fixed4 frag(v2f i) : SV_Target
{
float2 r = 2.0 * (i.uv - 0.5);
float aspectRatio = _ScreenParams.x / _ScreenParams.y;
r.x *= aspectRatio;

fixed3 bgCol = float3(1.0, 1.0, 1.0); // white

fixed3 col1 = float3(0.216, 0.471, 0.698); // blue
fixed3 col2 = float3(1.00, 0.329, 0.298); // red
fixed3 col3 = float3(0.867, 0.910, 0.247); // yellow

fixed3 ret;
ret = bgCol;



//第一部分,循环向上运动
if (i.uv.x < 1.0 / 5.0) 
{
float2 q = r + float2(aspectRatio*4.0 / 5.0, 0);

ret = fixed3(0.3, 0.3, 0.3);
//unity内置的时间向量
float y = _SpeedY*_Time.y;

//使得y在-1到1之间
y = mod(y,2.0) - 1.0;
ret = lerp(ret, col1, disk(q, float2(0.0, y), 0.1));
}
//第二部分，循环来回并缩放运动
else if (i.uv.x < 2.0 / 5.0) 
{
float2 q = r + float2(aspectRatio*2.0 / 5.0, 0);
ret = fixed3(0.4, 0.4, 0.4);
//添加振幅
float y = _Amplitude * sin(0.5*_Time.y* 2.0 * PI);
float radius = 0.15 + 0.05 * sin(_Time.y * 8.0);
ret = lerp(ret, col1, disk(q, float2(0.0, y), radius));
}
//第三部分，圆周运动并变换颜色
else if (i.uv.x < 3.0 / 5.0) 
{
float2 q = r + float2(aspectRatio * 0 / 5.0, 0);
ret = float3(0.5, 0.5, 0.5);

float x = _RAmplitudeX*cos(_Time.y*_RSpeedX);
float y = _RAmplitudeY*sin(_Time.y*_RSpeedY);
float radius = 0.2 + 0.1*sin(_Time.y*2.0);
fixed3 color = lerp(col1, col2, sin(_Time.y)*0.5 + 0.5);
ret = lerp(ret, color, rectangle(q, float2(x - 0.1, y - 0.1), float2(x + 0.1, y + 0.1)));
}
//第四部分，链条运动
else if (i.uv.x < 4.0 / 5.0) 
{
float2 q = r + float2(-aspectRatio*2.0 / 5.0, 0);
ret = float3(0.4, 0.4, 0.4);

for (float i = -1.0; i<1.0; i += 0.2)
{
float x = 0.2 * cos(_Time.y*_ChainAnimSpeed + i*PI);
float y = i;

float2 s = q - float2(x, y);
float angle = _Time.y * _ChainAnimRotaSpeed + i;
float2x2 rot = float2x2(cos(angle), -sin(angle),
sin(angle),  cos(angle));
s = mul(rot, s);
ret = lerp(ret, col1, rectangle(s, float2(-0.06, -0.06), float2(0.06, 0.06)));
}
}
//第五部分，跳跃运动
else if (i.uv.x < 5.0 / 5.0) 
{
float2 q = r + float2(-aspectRatio*4.0 / 5.0, 0);
ret = float3(0.3, 0.3, 0.3);

float speed = _JumpSpeed;
float t = _Time.y * speed;
float stopEveryAngle = PI / 2.0;
float stopRatio = 0.5;
//floor(x):返回小于等于t的最大整数     frac(x):返回x的小数部分
float t1 = (floor(t) + smoothstep(0.0, 1.0 - stopRatio, frac(t)))*stopEveryAngle;

float x = -0.2*cos(t1);
float y = 0.3 * sin(t1);
float dx = 0.1 + 0.03 * sin(t*10.0);
float dy = 0.1 + 0.03 * sin(t*10.0 + PI);
ret = lerp(ret, col1, rectangle(q, float2(x - dx, y - dy), float2(x + dx, y + dy)));


}


fixed3 pixel = ret;
return fixed4(pixel, 1.0);
}


ENDCG
}
}
}

代码中使用到了“_Time”变量，这个是Unity内置的四维向量，（t/20,t,t*2,t*3）因此“_Time.y=t”即获得系统的渲染的单位时间。
2、等离子流动效果，效果图如图所示：
Shader代码如下：

Shader "Unlit/Chapter6-Plasma"
{
Properties
{
_WaveSpeed("波浪速度",Range(0,10))=8
_ColorValue1("混合颜色1",Range(0,360))=180
_ColorValue2("混合颜色2",Range(0,360)) = 180
}
SubShader
{
// No culling or depth
Cull Off ZWrite Off ZTest Always
CGINCLUDE
#define PI 3.1415926
ENDCG


Pass
{
CGPROGRAM
#pragma vertex vert
#pragma fragment frag

#include "UnityCG.cginc"
uniform float _WaveSpeed;
uniform float _ColorValue1;
uniform float _ColorValue2;

struct appdata
{
float4 vertex : POSITION;
float2 uv : TEXCOORD0;
};

struct v2f
{
float2 uv : TEXCOORD0;
float4 vertex : SV_POSITION;
};

v2f vert(appdata v)
{
v2f o;
o.vertex = mul(UNITY_MATRIX_MVP, v.vertex);
o.uv = v.uv;
o.uv.y = 1 - o.uv.y;
return o;
}

//等离子效果
fixed4 frag(v2f i) : SV_Target
{
float2 r = 2.0 * (i.uv - 0.5);
float aspectRatio = _ScreenParams.x / _ScreenParams.y;
r.x *= aspectRatio;
float t = _Time.y*_WaveSpeed;
r = r*8.0;

float v1 = sin(r.x + t);
float v2 = sin(r.y + t);
float v3 = sin(r.x + r.y + t);
float v4 = sin(sqrt(r.x*r.x + r.y*r.y) + 1.7*t);
float v = v1 + v2 + v3 + v4;
fixed3 ret;

//第一部分垂直波浪
if (i.uv.x < 1.0 / 10.0) 
{
ret = float3(v1, v1, v1)
}
//第二部分水平波浪
else if (i.uv.x < 2.0 / 10.0)
{
ret = float3(v2, v2, v2);
}

//第三部分对角线波浪
else if (i.uv.x < 3.0 / 10.0) 
{
ret = float3(v3, v3, v3);
}
//第四部分圆环波浪
else if (i.uv.x < 4.0 / 10.0) 
{
ret = float3(v4, v4, v4);
}
//第五部分所有波浪的综合
else if (i.uv.x < 5.0 / 10.0) 
{
ret = float3(v, v, v);
}
//第六部分通过正、余弦函数添加周期性渐变
else if (i.uv.x < 6.0 / 10.0)
{
ret = float3(sin(2.0 * v), sin(2.0 * v), sin(2.0 * v));
}
//第七部分混合各种颜色
else if (i.uv.x < 10.0 / 10.0) 
{
ret = float3(sin(v), sin(v + _ColorValue1/PI), sin(v + _ColorValue2/PI));
}

ret = 0.5 + 0.5 * ret;

fixed3 pixel = ret;
return fixed4(pixel, 1.0);
}
ENDCG
}
}
}

四、总结

1、Cg函数虽简单，使用得当也是逼格暴涨，对于想学好Shader童鞋来讲，还是要多从Cg语言基础着手，通过实例练习，不仅可以巩固基础知识，而且也可以在做的过程中添加学习的信心和兴趣。2、正弦、余弦函数配合时间变量的使用能做到非常不错的动画效果，最好的效果还是要从根本上来讲还是数学，当今世界是学好数学和英语走遍天下都不怕了。