1.代码
r = sin(PI * r / 2)

Shader "Custom/AngleTwist"
{
    Properties
    {
        _MainTex ("Texture", 2D) = "white" {}
    }
    SubShader
    {
        Tags { "RenderType"="Opaque" }
        LOD 100

        Pass
        {
            CGPROGRAM
            #pragma vertex vert
            #pragma fragment frag

            #include "UnityCG.cginc"

            #define PI 3.14159265359

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

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

            sampler2D _MainTex;
            //这样定义不行
            //float PI = 3.1415926;

            v2f vert (appdata v)
            {
                v2f o;
                o.vertex = UnityObjectToClipPos(v.vertex);
                o.uv = v.uv;
                return o;
            }

            fixed4 frag (v2f i) : SV_Target
            {
                //i.uv -= 0.5;
                float2 center = float2(0.5,0.5);
                float r = length(i.uv - center);
                r = sin(PI * r / 2.0);
                float phi = atan2(i.uv.y - 0.5,i.uv.x - 0.5);
                i.uv.x = r * cos(phi) + 0.5;
                i.uv.y = r * sin(phi) + 0.5;
                // sample the texture
                fixed4 col = tex2D(_MainTex, i.uv);
                return col;
            }
            ENDCG
        }
    }
}

效果：

2.r = 2 * asin(r) / PI

Shader "Custom/AngleTwist"
{
    Properties
    {
        _MainTex ("Texture", 2D) = "white" {}
    }
    SubShader
    {
        Tags { "RenderType"="Opaque" }
        LOD 100

        Pass
        {
            CGPROGRAM
            #pragma vertex vert
            #pragma fragment frag

            #include "UnityCG.cginc"

            #define PI 3.14159265359

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

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

            sampler2D _MainTex;
            //这样定义不行
            //float PI = 3.1415926;

            v2f vert (appdata v)
            {
                v2f o;
                o.vertex = UnityObjectToClipPos(v.vertex);
                o.uv = v.uv;
                return o;
            }

            fixed4 frag (v2f i) : SV_Target
            {
                //i.uv -= 0.5;
                float2 center = float2(0.5,0.5);
                float r = length(i.uv - center);
                r = 2 * asin(r * 2) / PI;
                float phi = atan2(i.uv.y - 0.5,i.uv.x - 0.5);
                i.uv.x = r * cos(phi) + 0.5;
                i.uv.y = r * sin(phi) + 0.5;
                // sample the texture
                fixed4 col = tex2D(_MainTex, i.uv);
                return col;
            }
            ENDCG
        }
    }
}

效果:

注意：
定义常量用#define