Why my circle wave has a hole in the center ?

This is simplified version without light, the wave center is (0,0)

Code (CSharp):

1. Shader "Water/CircleWaveHasHole"
2. {
3.     Properties
4.     {
5.         _Color("Color", Color) = (1,1,1,1)
6.         _MainTex("Texture", 2D) = "white" {}
7.         [Gamma]_Metallic("Metallic", Range(0,1)) = 0
8.         _Smoothness("Smoothness", Range(0,1)) = 0
9.  
10.         _Wave1("Wave1  (ALQP)", Vector) = (0.2,5,0.2,1)//A:amplitude， L:wavelength， Q:steepness P：Initial phase
11.         _Center1("Wave1 Center", Vector) = (1,1,1,1)//
12.     }
13.     SubShader
14.     {
15.         Tags { "RenderType"="Opaque" }
16.         LOD 100
17.  
18.         Pass
19.         {
20.             CGPROGRAM
21.             #pragma vertex vert
22.             #pragma fragment frag
23.             // make fog work
24.             #pragma multi_compile_fog
25.  
26.             #include "UnityCG.cginc"
27.  
28.             #define TAU (2*UNITY_PI)
29.             #define TIME (_Time.y)
30.             struct GerstnerWave {
31.                 float amplitude;
32.                 float wavelength;
33.                 float speed;
34.                 float3 dir;
35.                 float4 center;
36.                 float steepness;
37.                 float w;
38.             };
39.  
40.             struct appdata
41.             {
42.                 float4 vertex : POSITION;
43.                 float2 uv : TEXCOORD0;
44.             };
45.  
46.             struct v2f
47.             {
48.                 float2 uv : TEXCOORD0;
49.                 float4 vertex : SV_POSITION;
50.             };
51.  
52.             sampler2D _MainTex;
53.             float4 _MainTex_ST;
54.             float4 _Color;
55.             float _Metallic;
56.             float _Smoothness;
57.  
58.             float4 _Wave1;
59.             float4 _Center1;
60.  
61.             void GerstnerPositionSum(float3 originalPoint, GerstnerWave wave, inout float3 positionOffset) {
62.                 float phi = dot(normalize(originalPoint.xz - float2(0, 0)), originalPoint.xz);
63.                 positionOffset.y += wave.amplitude*sin(phi);
64.             }
65.  
66.             v2f vert (appdata v)
67.             {
68.                 v2f o;
69.  
70.                 o.uv = TRANSFORM_TEX(v.uv, _MainTex);
71.  
72.                 GerstnerWave wave;
73.  
74.                 wave.amplitude = _Wave1[0];
75.                 wave.wavelength = _Wave1[1];
76.                 wave.steepness = _Wave1[2];
77.                 wave.speed = _Wave1[3];
78.                 wave.center = _Center1;
79.                 wave.w = TAU / wave.wavelength;
80.                 //float2 dir = abs(normalize(v.vertex.xz - _Center1.xz));
81.                 //waves[0].dir = (dir.x, 0, dir.y);
82.                 float3 positionOffset = float3(0, 0, 0);
83.                 GerstnerPositionSum(v.vertex, wave, positionOffset);
84.  
85.                 v.vertex.y += positionOffset.y;
86.                 o.vertex = UnityObjectToClipPos(v.vertex);
87.                 return o;
88.             }
89.  
90.             fixed4 frag (v2f i) : SV_Target
91.             {
92.                 return fixed4(0,0,0,0);
93.             }
94.             ENDCG
95.         }
96.     }
97. }
98.  

I don't know why has a hole in center, how can the vertex be deleted？

 

I suspect the problem is here: normalize(originalPoint.xz - float2(0, 0)). I bet your missing vertex is exactly at position 0, which means your are trying to normalize 0 which returns something that is either infinite or simply not a number. Either way, not something you want to use as a vertex position

 

Recently I have been quite busy, sorry, I forget to reply. I modify the code like this:

Code (CSharp):

1. float phi = 0;
2. if(originalPoint.x!=0 || originalPoint.z!=0 ){
3.     phi = dot(normalize(originalPoint.xz - float2(0, 0)), originalPoint.xz);
4. }

And I think if the wave is circle wave, use length(originalPoint.xz - float2(0, 0) is better.