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@muripo_lifein株式会社RICOS (RICOS Co. Ltd.)

GLSLレイマーチング研究_距離関数について勉強してみた19(Triangleの関数をいじる)

Last updated at Posted at 2017-04-17

modeling with distance functionsの距離関数の一覧に沿って記事を書いています.

距離関数は

float dot2( in vec3 v ) { return dot(v,v); }
float udTriangle( vec3 p, vec3 a, vec3 b, vec3 c )
{
    vec3 ba = b - a; vec3 pa = p - a;
    vec3 cb = c - b; vec3 pb = p - b;
    vec3 ac = a - c; vec3 pc = p - c;
    vec3 nor = cross( ba, ac );

    return sqrt(
        (sign(dot(cross(ba,nor),pa)) +
        sign(dot(cross(cb,nor),pb)) +
        sign(dot(cross(ac,nor),pc))<2.0)
        ?
        min( min(
        dot2(ba*clamp(dot(ba,pa)/dot2(ba),0.0,1.0)-pa),
        dot2(cb*clamp(dot(cb,pb)/dot2(cb),0.0,1.0)-pb) ),
        dot2(ac*clamp(dot(ac,pc)/dot2(ac),0.0,1.0)-pc) )
        :
        dot(nor,pa)*dot(nor,pa)/dot2(nor)
    );
}

image01.PNG

回転させてみる

float dot2( in vec3 v ) { return dot(v,v); }
float udTriangle( vec3 p, vec3 a, vec3 b, vec3 c )
{
    p = mat3(1.0,0,0, 0,cos(time),-sin(time), 0,sin(time),cos(time) )*p;
    p = mat3(cos(time),-sin(time),0, sin(time), cos(time),0 ,0,0,1)*p;

    vec3 ba = b - a; vec3 pa = p - a;
    vec3 cb = c - b; vec3 pb = p - b;
    vec3 ac = a - c; vec3 pc = p - c;
    vec3 nor = cross( ba, ac );

    return sqrt(
        (sign(dot(cross(ba,nor),pa)) +
        sign(dot(cross(cb,nor),pb)) +
        sign(dot(cross(ac,nor),pc))<2.0)
        ?
        min( min(
        dot2(ba*clamp(dot(ba,pa)/dot2(ba),0.0,1.0)-pa),
        dot2(cb*clamp(dot(cb,pb)/dot2(cb),0.0,1.0)-pb) ),
        dot2(ac*clamp(dot(ac,pc)/dot2(ac),0.0,1.0)-pc) )
        :
        dot(nor,pa)*dot(nor,pa)/dot2(nor)
    );
}

motion01.gif

Triangular Prismに変形させてみる

float dot2( in vec3 v ) { return dot(v,v); }
float udTriangle( vec3 p, vec3 a, vec3 b, vec3 c )
{
    vec3 ba = b - a; vec3 pa = p - a;
    vec3 cb = c - b; vec3 pb = p - b;
    vec3 ac = a - c; vec3 pc = p - c;
    vec3 nor = cross( ba, ac );

    return sqrt(
        (sign(dot(cross(ba,nor),pa)) +
        sign(dot(cross(cb,nor),pb)) +
        sign(dot(cross(ac,nor),pc))<2.0)
        ?
        min( min(
        dot2(ba*clamp(dot(ba,pa)/dot2(ba),0.0,1.0)-pa),
        dot2(cb*clamp(dot(cb,pb)/dot2(cb),0.0,1.0)-pb) ),
        dot2(ac*clamp(dot(ac,pc)/dot2(ac),0.0,1.0)-pc) )
        :
        dot(nor,pa)*dot(nor,pa)/dot2(nor)
    );
}

float sdTriPrism(vec3 p)
{
    float radio = 1.0; // 一辺の長さ
    float hight = 1.0; // 厚さ（高さ
    // Triangular Prism1
    return max(abs(p.z)-hight,max(abs(p.x)*0.866025+p.y*0.5, -p.y)-radio);
}

float udInstanceTriangle(in vec3 p)
{
    p = mat3(1.0,0,0, 0,cos(time),-sin(time), 0,sin(time),cos(time) )*p;
    p = mat3(cos(time),-sin(time),0, sin(time), cos(time),0 ,0,0,1)*p;
    return udTriangle(p, vec3(0.0, 0.5, 1.0), vec3(0.2, 1.0, 0.9), vec3(0.9, 0.2, 0.1) )*abs(sin(time))+sdTriPrism(p)*(1.0-abs(sin(time)));
}

motion02.gif

sphereに変化形させてみる.

float dot2( in vec3 v ) { return dot(v,v); }
float udTriangle( vec3 p, vec3 a, vec3 b, vec3 c )
{
    vec3 ba = b - a; vec3 pa = p - a;
    vec3 cb = c - b; vec3 pb = p - b;
    vec3 ac = a - c; vec3 pc = p - c;
    vec3 nor = cross( ba, ac );

    return sqrt(
        (sign(dot(cross(ba,nor),pa)) +
        sign(dot(cross(cb,nor),pb)) +
        sign(dot(cross(ac,nor),pc))<2.0)
        ?
        min( min(
        dot2(ba*clamp(dot(ba,pa)/dot2(ba),0.0,1.0)-pa),
        dot2(cb*clamp(dot(cb,pb)/dot2(cb),0.0,1.0)-pb) ),
        dot2(ac*clamp(dot(ac,pc)/dot2(ac),0.0,1.0)-pc) )
        :
        dot(nor,pa)*dot(nor,pa)/dot2(nor)
    );
}

float sdSphere( vec3 p)
{
    return length(p)-1.0;
}

float udInstanceTriangle(in vec3 p)
{
    p = mat3(1.0,0,0, 0,cos(time),-sin(time), 0,sin(time),cos(time) )*p;
    p = mat3(cos(time),-sin(time),0, sin(time), cos(time),0 ,0,0,1)*p;
    return udPlayTriangle(p, vec3(0.0, 0.5, 1.0), vec3(0.2, 1.0, 0.9), vec3(0.9, 0.2, 0.1) )*sin(time)+sdSphere(p)*(1.0-sin(time));
}

motion03.gif

ちなみに合成は、

\sin(time)*距離関数1 + (1-\sin(time))*距離関数2

で、合成しています。

コード 

// ============================================================================
// Triangle
// ============================================================================

precision mediump float;
uniform vec2 resolution;     // resolution (512.0, 512.0)
uniform vec2 mouse;          // mouse(-1.0 ~ 1.0)
uniform float time;          // time(1second == 1.0)
uniform sampler2D prevScene; // previous scene texture

float sdSphere( vec3 p)
{
    return length(p)-1.0;
}

float sdTriPrism(vec3 p)
{
    float radio = 1.0; // 一辺の長さ
    float hight = 1.0; // 厚さ（高さ
    // Triangular Prism1
    return max(abs(p.z)-hight,max(abs(p.x)*0.866025+p.y*0.5, -p.y)-radio);
}

float dot2( in vec3 v ) { return dot(v,v); }
float udTriangle( vec3 p, vec3 a, vec3 b, vec3 c )
{
    vec3 ba = b - a; vec3 pa = p - a;
    vec3 cb = c - b; vec3 pb = p - b;
    vec3 ac = a - c; vec3 pc = p - c;
    vec3 nor = cross( ba, ac );

    return sqrt(
        (sign(dot(cross(ba,nor),pa)) +
        sign(dot(cross(cb,nor),pb)) +
        sign(dot(cross(ac,nor),pc))<2.0)
        ?
        min( min(
        dot2(ba*clamp(dot(ba,pa)/dot2(ba),0.0,1.0)-pa),
        dot2(cb*clamp(dot(cb,pb)/dot2(cb),0.0,1.0)-pb) ),
        dot2(ac*clamp(dot(ac,pc)/dot2(ac),0.0,1.0)-pc) )
        :
        dot(nor,pa)*dot(nor,pa)/dot2(nor)
    );
}

float udPlayTriangle( vec3 p, vec3 a, vec3 b, vec3 c )
{
    vec3 ba = b - a; vec3 pa = p - a;
    vec3 cb = c - b; vec3 pb = p - b;
    vec3 ac = a - c; vec3 pc = p - c;
    vec3 nor = cross( ba, ac );

    return sqrt(
        (sign(dot(cross(ba,nor),pa)) +
        sign(dot(cross(cb,nor),pb)) +
        sign(dot(cross(ac,nor),pc))<2.0)
//      sign(dot(cross(ac,nor),pc))<2.0*sin(time))
        ?
        min( min(
//      min( max(
//      max( min(
//      max( max(
        dot2(ba*clamp(dot(ba,pa)/dot2(ba),0.0,1.0)-pa),
//      dot2(ba*min(max(dot(ba,pa)/dot2(ba),0.0),1.0)-pa),
//      dot2(ba*min(max(dot(ba,pa)/dot2(ba),0.0),sin(time))-pa),
//      dot2(ba*clamp(dot(ba,pa)/dot2(ba),0.0,1.0)-pa),

        dot2(cb*clamp(dot(cb,pb)/dot2(cb),0.0,1.0)-pb) ),
        dot2(ac*clamp(dot(ac,pc)/dot2(ac),0.0,1.0)-pc) )
        :
        dot(nor,pa)*dot(nor,pa)/dot2(nor)
//      dot(nor,pa)*dot(nor,pa)/dot2(nor)*abs(sin(time))
    );
}

float udInstanceTriangle(in vec3 p)
{
//  p = mat3(1.0,0,0, 0,cos(1.57),-sin(1.57), 0,sin(1.57),cos(1.57) )*p;
    p = mat3(1.0,0,0, 0,cos(time),-sin(time), 0,sin(time),cos(time) )*p;
    // p = mat3(cos(time),0,-sin(time), 0,1,0, sin(time),0,cos(time))*p;
    p = mat3(cos(time),-sin(time),0, sin(time), cos(time),0 ,0,0,1)*p;
//  return udTriangle(p, vec3(0.0, 0.5, 1.0), vec3(0.2, 0.8, 0.5), vec3(0.9, 0.3, 0.4) );
//  return udPlayTriangle(p, vec3(0.0, 0.5, 1.0), vec3(0.2, 0.8, 0.5), vec3(0.9, 0.3, 0.4) );
//  return udPlayTriangle(p, vec3(0.0, 0.5, 1.0), vec3(0.2, 1.0, 0.9), vec3(0.9, 0.2, 0.1) );
//  return udPlayTriangle(p, vec3(0.0, 0.5, 1.0), vec3(0.2, 1.0, 0.9), vec3(0.9, 0.2, 0.1) )*sin(time)+sdSphere(p)*(1.0-sin(time));
    return udPlayTriangle(p, vec3(0.0, 0.5, 1.0), vec3(0.2, 1.0, 0.9), vec3(0.9, 0.2, 0.1) )*abs(sin(time))+sdTriPrism(p)*(1.0-abs(sin(time)));
}

float distanceHub(vec3 p){
    // 0.4を書けて、rayの進行を遅らせている
    return udInstanceTriangle(p)*0.4;
}

// 法線
vec3 genNormal(vec3 p){
    float d = 0.001;
    // 法線を生成
    return normalize(vec3(
        distanceHub(p + vec3(  d, 0.0, 0.0)) - distanceHub(p + vec3( -d, 0.0, 0.0)),
        distanceHub(p + vec3(0.0,   d, 0.0)) - distanceHub(p + vec3(0.0,  -d, 0.0)),
        distanceHub(p + vec3(0.0, 0.0,   d)) - distanceHub(p + vec3(0.0, 0.0,  -d))
    ));
}

// 図形ごとに色をわける
vec3 doColor(vec3 p){
    float e = 0.001;
    if (udInstanceTriangle(p)<e){
        vec3 normal = genNormal(p);
        vec3 light  = normalize(vec3(1.0, 1.0, 1.0));
        float diff  = max(dot(normal, light), 0.1);
        return vec3(diff, diff, diff);
    }
    return vec3(0.0);
}

// カメラのワーク
void main(){
    // スクリーンスペースを考慮して座標を正規化
    vec2 p = (gl_FragCoord.xy * 2.0 - resolution) / min(resolution.x, resolution.y);
    // カメラを定義
    vec3 cPos  = vec3(0.0, 0.0,  3.0);   // カメラの位置
    vec3 cDir  = vec3(0.0, 0.0, -1.0);   // カメラの向き(視線)
    vec3 cUp   = vec3(0.0, 1.0,  0.0);   // カメラの上方向
    vec3 cSide = cross(cDir, cUp);       // 外積を使って横方向を算出
    float targetDepth = 1.0;             // フォーカスする深度

    // カメラの情報からレイを定義
    vec3 ray = normalize(cSide * p.x + cUp * p.y + cDir * targetDepth);
    // マーチングループを組む
    float dist = 0.0; // レイとオブジェクト間の最短距離
    float rLen = 0.0; // レイに継ぎ足す長さ
    vec3 rPos = cPos; // レイの先端位置(初期位置)

    // レイが進む処理(マーチングループ)
    for(int i = 0; i < 32; ++i){
        dist = distanceHub(rPos);
        rLen += dist;
        rPos = cPos + ray * rLen;
    }

    // レイとオブジェクトの距離を確認
    vec3 color = doColor(rPos);
    gl_FragColor = vec4(color, 1.0);
}
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