shader utils

https://qiita.com/keim_at_si/items/c2d1afd6443f3040e900 HSV

https://docs.unity3d.com/ja/2017.4/Manual/SL-UnityShaderVariables.html

ビルトインシェーダ変数 

プロジェクション行列の逆行列

unity_CameraInvProjection

カメラのアスペクト比の取得

https://qiita.com/Santarh/items/428d2e0f33852e6f37b5

//h-色,s-明暗,v-色の強さ
float3 HSVRGB(float h,float s,float v){
	return ((clamp(abs(frac(h+float3(0,2,1)/3.)*6.-3.)-1.,0.,1.)-1.)*s+1.)*v;
}
    
    
//カメラのアスペクト比
float2 Aspect(){
	float4 projectionSpaceUpperRight = float4(1, 1, UNITY_NEAR_CLIP_VALUE, _ProjectionParams.y);
	float4 viewSpaceUpperRight = mul(unity_CameraInvProjection, projectionSpaceUpperRight);
	return float2(viewSpaceUpperRight.x,viewSpaceUpperRight.y);
}

//外積-法線方向    
float4 v1 = vg[1].vertex - vg[0].vertex;
float4 v2 = vg[2].vertex - vg[0].vertex;
float3 nor = cross(v1,v2);


//四角の中かどうかを判定する関数
bool IsInBox(float2 p,float2 center,float2 size){
 size /= 2;
 p = center-p;
 float len = max(abs(p.x) - size.x, abs(p.y) - size.y);
 return len<0.001 ? true : false;
}

float3 CameraDir(){
	return UNITY_MATRIX_IT_MV[2].xyz;
}

void LookAtRot(inout float4 pnt,float3 at){
	pnt.w = 1;
	float3 z = normalize(at - pnt.xyz);
	float3 x = normalize(cross(float3(0,1,0),z));
	float3 y = normalize(cross(z,x));
	float4x4 rot = float4x4(x.x, y.x, z.x, 0,
	                        x.y, y.y, z.y, 0,
							x.z, y.z, z.z, 0,
							0,   0,   0, 1);
	pnt = mul(rot,pnt);
}

//Position値
float3 GetWorldPos(){
	float4x4 mt = unity_ObjectToWorld;
	return mul(unity_ObjectToWorld,float4(0,0,0,1));
}

//Scale値
float3 GetWorldScale(){
	float4x4 mt = unity_ObjectToWorld;
	return float3(length(float3(mt._m00,mt._m01,mt._m02)), length(float3(mt._m10,mt._m11,mt._m12)), length(float3(mt._m20,mt._m21,mt._m22)));
}

//Unityの回転はZXYの順番で行われてるらしい
http://light11.hatenadiary.com/entry/2019/01/24/223705

float4 Rot(float4 pos,float3 rot){
	float rdc = UNITY_PI/180;
	return RotY(RotX(RotZ(pos,rdc*rot.z),rdc*rot.x),rdc*rot.y);
}


float4 RotX(float4 pos,float rad){
  return mul(float4x4(1,0,0,0, 0,cos(rad),-sin(rad),0,  0,sin(rad),cos(rad),0, 0,0,0,1),pos);
}

float4 RotY(float4 pos,float rad){
  return mul(float4x4(cos(rad),0,sin(rad),0, 0,1,0,0, -sin(rad),0,cos(rad),0, 0,0,0,1),pos);
}

float4 RotZ(float4 pos,float rad){
  return mul(float4x4(cos(rad),-sin(rad),0,0, sin(rad),cos(rad),0,0, 0,0,1,0, 0,0,0,1),pos);
}

float2 Rot2D(float2 xy,float rad){
  rad *= UNITY_PI/180;
  xy = xy*2-1;
  float2x2 rot = float2x2(cos(rad),-sin(rad),sin(rad),cos(rad));
  xy = mul(rot,xy);
  return xy/2 + 0.5;
}

float2 Rot2D(float2 xy,float rad){
 //rad *= UNITY_PI/180;
 float2x2 rot = float2x2(cos(rad),-sin(rad),sin(rad),cos(rad));
 return mul(rot,xy);
}

//-1 => 1 => -1 を繰り返す
uint tt = trunc(_Time.y);
float ft = frac(_Time.y),rt = tt%4;
if(rt == 0){ rt = -1 + ft;}
else if(rt == 1){ rt = ft;}
else if(rt == 2){ rt = 1 - ft;}
else if(rt == 3){ rt = -ft;}

    
//0=>1=>0を繰り返す    
float t_id = frac(_Time.y);
t_id = t_id<=0.5 ? t_id*2 : 1 - (t_id-0.5)*2;

float4 HSVToRGB(float4 hsv){
	float4 K = float4(1.0, 2.0 / 3.0, 1.0 / 3.0, 3.0);
	float3 p = abs(frac(hsv.xxx + K.xyz) * 6.0 - K.www);
	float3 o = hsv.z * lerp(K.xxx, saturate(p - K.xxx), hsv.y);
	return float4(o.rgb,hsv.a);
}

float4 RGBToHSV(float4 c){
	float4 K = float4(0.0, -1.0 / 3.0, 2.0 / 3.0, -1.0);
	float4 p = lerp(float4(c.bg, K.wz), float4(c.gb, K.xy), step(c.b, c.g));
	float4 q = lerp(float4(p.xyw, c.r), float4(c.r, p.yzx), step(p.x, c.r));
	float d = q.x - min(q.w, q.y);
    float e = 1.0e-10;
    return float4(abs(q.z + (q.w - q.y) / (6.0 * d + e)), d / (q.x + e), q.x,c.a);
}

    
    
float3 hsv2rgb(float3 hsv){
    float4 K = float4(1.0, 2.0 / 3.0, 1.0 / 3.0, 3.0);
    float3 p = abs(frac(hsv.xxx + K.xyz) * 6.0 - K.www);
    return hsv.z * lerp(K.xxx, saturate(p - K.xxx), hsv.y);
}

float rand(float2 co){
  co = fmod(co,10000);
  return frac(sin(dot(co.xy ,float2(12.9898,78.233))) * 43758.5453);
}

float GetNumByTime(float digit,float change_frec){
	int d = trunc(digit);
	float tm = _Time.y/changeFrec*Pow(10,d);//小数部をd桁分、整数部に移動
	float mx = trunc(tm);//小数部切り捨て
	return frac(mx/10000);//整数部5桁を小数部に移動,整数部切り捨て
}
float Pow(float val,int times){
	float res = 1;
	for(int k=0;k<times;k++){
		res *= val;
	}
	return res;
}
//階上
int upstairs(int top,int num){
	int res = 1;
	for(int i=0;i<num;i++){
		res *= top - i;
	}
	return res;

//二項係数
//nCk  https://mathtrain.jp/nikouteiri
int coef(int n ,int k){
	return upstairs(n,k) / upstairs(k,k);
}

//ガンマ関数による階乗
//z>0.5とする
//これ合ってるのか分からん
//元ネタは以下のc#の実装
//https://rosettacode.org/wiki/Gamma_function#C.23
float Ganma(float z){
	z -= 1;
	float x = 0.99999999999980993;
	x += 676.5203681218851/(z+1);
	x += -1259.1392167224028/(z+2);
	x += 771.32342877765313/(z+3);
	x += -176.61502916214059/(z+4);
	x += 12.507343278686905/(z+5);
	x += -0.13857109526572012/(z+6);
	x += 9.9843695780195716e-6/(z+7);
	x += 1.5056327351493116e-7/(z+8);
	float t = z + 7 + 0.5;
	return sqrt(2*PI)*pow(t,z+0.5)*pow(NAPIER,-t)*x;
}