用代码来画画 —— Ray-Marching（光线步进） 多个立体图形的绘制【GLSL】

参考自： 

iq 的 https://www.shadertoy.com/view/Xds3zN

http://www.iquilezles.org/www/articles/distfunctions/distfunctions.htm

http://www.iquilezles.org/www/articles/rmshadows/rmshadows.htm

http://ogldev.atspace.co.uk/www/tutorial13/tutorial13.html

http://9bitscience.blogspot.kr/2013/07/raymarching-distance-fields_14.html

完整代码及算法详细注释：

// Created by inigo quilez - iq/2013// License Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.// A list of usefull distance function to simple primitives, and an example on how to// do some interesting boolean operations, repetition and displacement.//// More info here: http://www.iquilezles.org/www/articles/distfunctions/distfunctions.htm// https://www.shadertoy.com/view/Xds3zN// 抗锯齿开关#define AA 2   // make this 1 is your machine is too slow//------------------------------------------------------------------// --------SDF--------// http://www.iquilezles.org/www/articles/distfunctions/distfunctions.htmfloat sdPlane(vec3 p){return p.y;}float sdSphere(vec3 p, float s){return length(p) - s;}float sdBox(vec3 p, vec3 b){vec3 d = abs(p) - b;return min(max(d.x, max(d.y, d.z)), 0.0) + length(max(d, 0.0));}float sdEllipsoid( in vec3 p, in vec3 r ){return (length( p/r ) - 1.0) * min(min(r.x,r.y),r.z);}float udRoundBox(vec3 p, vec3 b, float r){return length(max(abs(p) - b, 0.0)) - r;}float sdTorus(vec3 p, vec2 t){return length(vec2(length(p.xz) - t.x, p.y)) - t.y;}float sdHexPrism(vec3 p, vec2 h){vec3 q = abs(p);#if 0return max(q.z-h.y,max((q.x*0.866025+q.y*0.5),q.y)-h.x);#elsefloat d1 = q.z - h.y;float d2 = max((q.x * 0.866025 + q.y * 0.5), q.y) - h.x;return length(max(vec2(d1, d2), 0.0)) + min(max(d1, d2), 0.);#endif}float sdCapsule(vec3 p, vec3 a, vec3 b, float r){vec3 pa = p - a, ba = b - a;float h = clamp(dot(pa, ba) / dot(ba, ba), 0.0, 1.0);return length(pa - ba * h) - r;}float sdTriPrism(vec3 p, vec2 h){vec3 q = abs(p);#if 0return max(q.z-h.y,max(q.x*0.866025+p.y*0.5,-p.y)-h.x*0.5);#elsefloat d1 = q.z - h.y;float d2 = max(q.x * 0.866025 + p.y * 0.5, -p.y) - h.x * 0.5;return length(max(vec2(d1, d2), 0.0)) + min(max(d1, d2), 0.);#endif}float sdCylinder(vec3 p, vec2 h){vec2 d = abs(vec2(length(p.xz), p.y)) - h;return min(max(d.x, d.y), 0.0) + length(max(d, 0.0));}float sdCone( in vec3 p, in vec3 c ){vec2 q = vec2( length(p.xz), p.y );float d1 = -q.y-c.z;float d2 = max( dot(q,c.xy), q.y);return length(max(vec2(d1,d2),0.0)) + min(max(d1,d2), 0.);}float sdConeSection( in vec3 p, in float h, in float r1, in float r2 ){float d1 = -p.y - h;float q = p.y - h;float si = 0.5*(r1-r2)/h;float d2 = max( sqrt( dot(p.xz,p.xz)*(1.0-si*si)) + q*si - r2, q );return length(max(vec2(d1,d2),0.0)) + min(max(d1,d2), 0.);}float sdPryamid4(vec3 p, vec3 h) // h = { cos a, sin a, height }{// Tetrahedron = Octahedron - Cubefloat box = sdBox(p - vec3(0, -2.0 * h.z, 0), vec3(2.0 * h.z));float d = 0.0;d = max(d, abs(dot(p, vec3(-h.x, h.y, 0))));d = max(d, abs(dot(p, vec3(h.x, h.y, 0))));d = max(d, abs(dot(p, vec3(0, h.y, h.x))));d = max(d, abs(dot(p, vec3(0, h.y, -h.x))));float octa = d - h.z;return max(-box, octa); // Subtraction}// --------SDF--------// (p.x^2 + p.y^2)^(1/2)float length2(vec2 p){return sqrt(p.x * p.x + p.y * p.y);}// (p.x^6 + p.y^6)^(1/6)float length6(vec2 p){p = p * p * p;p = p * p;return pow(p.x + p.y, 1.0 / 6.0);}// (p.x^8 + p.y^8)^(1/8)float length8(vec2 p){p = p * p;p = p * p;p = p * p;return pow(p.x + p.y, 1.0 / 8.0);}float sdTorus82(vec3 p, vec2 t){vec2 q = vec2(length2(p.xz) - t.x, p.y);return length8(q) - t.y;}float sdTorus88(vec3 p, vec2 t){vec2 q = vec2(length8(p.xz) - t.x, p.y);return length8(q) - t.y;}float sdCylinder6(vec3 p, vec2 h){return max(length6(p.xz) - h.x, abs(p.y) - h.y);}//------------------------------------------------------------------// Subtractionfloat opS(float d1, float d2){return max(-d2, d1);}// Unionvec2 opU(vec2 d1, vec2 d2){return (d1.x < d2.x) ? d1 : d2;}// Repetitionvec3 opRep(vec3 p, vec3 c){return mod(p, c) - 0.5 * c;}// Twistvec3 opTwist(vec3 p){float c = cos(10.0 * p.y + 10.0);float s = sin(10.0 * p.y + 10.0);mat2 m = mat2(c, -s, s, c);return vec3(m * p.xz, p.y);}//------------------------------------------------------------------vec2 map( in vec3 pos ){// res.x 是光线到表面的距离，res.y 影响的是物体材质vec2 res = opU( vec2( sdPlane( pos), 1.0 ),vec2( sdSphere( pos-vec3( 0.0,0.25, 0.0), 0.25 ), 46.9 ) );res = opU( res, vec2( sdBox( pos-vec3( 1.0,0.25, 0.0), vec3(0.25) ), 3.0 ) );res = opU( res, vec2( udRoundBox( pos-vec3( 1.0,0.25, 1.0), vec3(0.15), 0.1 ), 41.0 ) );res = opU( res, vec2( sdTorus( pos-vec3( 0.0,0.25, 1.0), vec2(0.20,0.05) ), 25.0 ) );res = opU( res, vec2( sdCapsule( pos,vec3(-1.3,0.10,-0.1), vec3(-0.8,0.50,0.2), 0.1 ), 31.9 ) );res = opU( res, vec2( sdTriPrism( pos-vec3(-1.0,0.25,-1.0), vec2(0.25,0.05) ),43.5 ) );res = opU( res, vec2( sdCylinder( pos-vec3( 1.0,0.30,-1.0), vec2(0.1,0.2) ), 8.0 ) );res = opU( res, vec2( sdCone( pos-vec3( 0.0,0.50,-1.0), vec3(0.8,0.6,0.3) ), 55.0 ) );res = opU( res, vec2( sdTorus82( pos-vec3( 0.0,0.25, 2.0), vec2(0.20,0.05) ),50.0 ) );res = opU( res, vec2( sdTorus88( pos-vec3(-1.0,0.25, 2.0), vec2(0.20,0.05) ),43.0 ) );res = opU( res, vec2( sdCylinder6( pos-vec3( 1.0,0.30, 2.0), vec2(0.1,0.2) ), 12.0 ) );res = opU( res, vec2( sdHexPrism( pos-vec3(-1.0,0.20, 1.0), vec2(0.25,0.05) ),17.0 ) );res = opU( res, vec2( sdPryamid4( pos-vec3(-1.0,0.15,-2.0), vec3(0.8,0.6,0.25) ),37.0 ) );res = opU( res, vec2( opS( udRoundBox( pos-vec3(-2.0,0.2, 1.0), vec3(0.15),0.05),sdSphere( pos-vec3(-2.0,0.2, 1.0), 0.25)), 13.0 ) );res = opU( res, vec2( opS( sdTorus82( pos-vec3(-2.0,0.2, 0.0), vec2(0.20,0.1)),sdCylinder( opRep( vec3(atan(pos.x+2.0,pos.z)/6.2831, pos.y, 0.02+0.5*length(pos-vec3(-2.0,0.2, 0.0))), vec3(0.05,1.0,0.05)), vec2(0.02,0.6))), 51.0 ) );res = opU( res, vec2( 0.5*sdSphere( pos-vec3(-2.0,0.25,-1.0), 0.2 ) + 0.03*sin(50.0*pos.x)*sin(50.0*pos.y)*sin(50.0*pos.z), 65.0 ) );res = opU( res, vec2( 0.5*sdTorus( opTwist(pos-vec3(-2.0,0.25, 2.0)),vec2(0.20,0.05)), 46.7 ) );res = opU( res, vec2( sdConeSection( pos-vec3( 0.0,0.35,-2.0), 0.15, 0.2, 0.1 ), 13.67 ) );res = opU( res, vec2( sdEllipsoid( pos-vec3( 1.0,0.35,-2.0), vec3(0.15, 0.2, 0.05) ), 43.17 ) );return res;}// 实际是 Ray-marchingvec2 castRay( in vec3 ro, in vec3 rd ){float tmin = 1.0;float tmax = 20.0;#if 1   // 加速 Raymarching// bounding volumefloat tp1 = (0.0-ro.y)/rd.y;if( tp1>0.0 )tmax = min( tmax, tp1 );float tp2 = (1.6-ro.y)/rd.y;if( tp2>0.0 ){if( ro.y>1.6 )tmin = max( tmin, tp2 );elsetmax = min( tmax, tp2 );}#endiffloat t = tmin;float m = -1.0;for( int i=0; i<64; i++ ){float precis = 0.0005*t;vec2 res = map( ro+rd*t );if( res.x<precis || t>tmax )break;t += res.x;m = res.y;// 唯一用到 res.y 的地方，影响材质的计算}if( t>tmax )m=-1.0;return vec2( t, m );}// 柔化阴影// http://www.iquilezles.org/www/articles/rmshadows/rmshadows.htmfloat softshadow( in vec3 ro, in vec3 rd, in float mint, in float tmax ){float res = 1.0;float t = mint;for( int i=0; i<16; i++ ){float h = map( ro + rd*t ).x;res = min( res, 8.0*h/t );t += clamp( h, 0.02, 0.10 );if( h<0.001 || t>tmax )// 在[ mint, maxt)范围内进行插值break;}return clamp( res, 0.0, 1.0 );}// 法线vec3 calcNormal( in vec3 pos ){vec2 e = vec2(1.0,-1.0)*0.5773*0.0005;return normalize( e.xyy*map( pos + e.xyy ).x +e.yyx*map( pos + e.yyx ).x +e.yxy*map( pos + e.yxy ).x +e.xxx*map( pos + e.xxx ).x );/* vec3 eps = vec3( 0.0005, 0.0, 0.0 ); vec3 nor = vec3( map(pos+eps.xyy).x - map(pos-eps.xyy).x, map(pos+eps.yxy).x - map(pos-eps.yxy).x, map(pos+eps.yyx).x - map(pos-eps.yyx).x ); return normalize(nor); */}// Ambient Occlusion: 环境光吸收/遮蔽float calcAO( in vec3 pos, in vec3 nor ){float occ = 0.0;float sca = 1.0;for( int i=0; i<5; i++ ){float hr = 0.01 + 0.12*float(i)/4.0;vec3 aopos = nor * hr + pos;float dd = map( aopos ).x;occ += -(dd-hr)*sca;sca *= 0.95;}return clamp( 1.0 - 3.0*occ, 0.0, 1.0 );}vec3 render( in vec3 ro, in vec3 rd ){vec3 col = vec3(0.7, 0.9, 1.0) +rd.y*0.8;vec2 res = castRay(ro,rd);float t = res.x;float m = res.y;if( m>-0.5 ){vec3 pos = ro + t*rd;// 步进的光线位置vec3 nor = calcNormal( pos );// 法线vec3 ref = reflect( rd, nor );// 反光// materialcol = 0.45 + 0.35*sin( vec3(0.05,0.08,0.10)*(m-1.0) );// 如果是地板的话if( m<1.5 ){// 格子地砖float f = mod( floor(5.0*pos.z) + floor(5.0*pos.x), 2.0);col = 0.3 + 0.1*f*vec3(1.0);}// 光照模型的计算float occ = calcAO( pos, nor );vec3 lig = normalize( vec3(-0.4, 0.7, -0.6) );float amb = clamp( 0.5+0.5*nor.y, 0.0, 1.0 );float dif = clamp( dot( nor, lig ), 0.0, 1.0 );float bac = clamp( dot( nor, normalize(vec3(-lig.x,0.0,-lig.z))), 0.0, 1.0 )*clamp( 1.0-pos.y,0.0,1.0);float dom = smoothstep( -0.1, 0.1, ref.y );float fre = pow( clamp(1.0+dot(nor,rd),0.0,1.0), 2.0 );float spe = pow(clamp( dot( ref, lig ), 0.0, 1.0 ),16.0);// 散射阴影dif *= softshadow( pos, lig, 0.02, 2.5 );// 反光阴影dom *= softshadow( pos, ref, 0.02, 2.5 );// 注意物体底座的阴影变化// occ = 1.;vec3 lin = vec3(0.0);lin += 1.30*dif*vec3(1.00,0.80,0.55);lin += 2.00*spe*vec3(1.00,0.90,0.70)*dif;lin += 0.40*amb*vec3(0.40,0.60,1.00)*occ;lin += 0.50*dom*vec3(0.40,0.60,1.00)*occ;lin += 0.50*bac*vec3(0.25,0.25,0.25)*occ;lin += 0.25*fre*vec3(1.00,1.00,1.00)*occ;col = col*lin;col = mix( col, vec3(0.8,0.9,1.0), 1.0-exp( -0.0002*t*t*t ) );}return vec3( clamp(col,0.0,1.0) );}mat3 setCamera( in vec3 ro, in vec3 ta, float cr ){vec3 cw = normalize(ta-ro);// lookvec3 cp = vec3(sin(cr), cos(cr),0.0);// XY Spacevec3 cu = normalize( cross(cw,cp) );// rightvec3 cv = normalize( cross(cu,cw) );// up// right,// up,* world = camera// look// 注意： glsl 是按列存储，所以可以直接右乘相机坐标系的点，结果就是世界坐标系下的点return mat3( cu, cv, cw );// right, up, look}uniform vec2 iMouse;uniform float iGlobalTime;const vec2 iResolution = vec2(512., 512.);#define fragColor gl_FragColor#define fragCoord  gl_FragCoordvoid main(){vec2 mo = iMouse.xy / iResolution.xy;float time = 15.0 + iGlobalTime;vec3 tot = vec3(0.0);#if AA>1// 开启 AAfor (int m = 0; m < AA; m++){for (int n = 0; n < AA; n++){// pixel coordinatesvec2 o = vec2(float(m), float(n)) / float(AA) - 0.5;vec2 p = (-iResolution.xy + 2.0 * (fragCoord + o)) / iResolution.y;#elsevec2 p = (-iResolution.xy + 2.0*fragCoord)/iResolution.y;#endif// cameravec3 ro = vec3(-0.5 + 3.5 * cos(0.1 * time + 6.0 * mo.x),1.0 + 2.0 * mo.y, 0.5 + 4.0 * sin(0.1 * time + 6.0 * mo.x));vec3 ta = vec3(-0.5, -0.4, 0.5);// camera-to-world transformationmat3 ca = setCamera(ro, ta, 0.0);// ray directionvec3 rd = ca * normalize(vec3(p.xy, 2.0));// rendervec3 col = render(ro, rd);// 针对电子屏幕的 gamma 矫正（否则颜色偏暗）col = pow(col, vec3(0.4545));tot += col;#if AA>1}}tot /= float(AA * AA);#endiffragColor = vec4(tot, 1.0);}