**URL**: http://glslsandbox.com/e#29798.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 |
// Ray Marching Tutorial (With Shading) // By: Brandon Fogerty // bfogerty at gmail dot com // xdpixel.com // Ray Marching is a technique that is very similar to Ray Tracing. // In both techniques, you cast a ray and try to see if the ray intersects // with any geometry. Both techniques require that geometry in the scene // be defined using mathematical formulas. However the techniques differ // in how the geometry is defined mathematically. As for ray tracing, // we have to define geometry using a formula that calculates the exact // point of intersection. This will give us the best visual result however // some types of geometry are very hard to define in this manner. // Ray Marching using distance fields to decribe geometry. This means all // we need to know to define a kind of geometry is how to mearsure the distance // from any arbitrary 3d position to a point on the geometry. We iterate or "march" // along a ray until one of two things happen. Either we get a resulting distance // that is really small which means we are pretty close to intersecting with some kind // of geometry or we get a really huge distance which most likely means we aren't // going to intersect with anything. // Ray Marching is all about approximating our intersection point. We can take a pretty // good guess as to where our intersection point should be by taking steps along a ray // and asking "Are we there yet?". The benefit to using ray marching over ray tracing is // that it is generally much easier to define geometry using distance fields rather than // creating a formula to analytically find the intersection point. Also, ray marching makes // certain effects like ambient occlusion almost free. It is a little more work to compute // the normal for geometry. I will cover more advanced effects using ray marching in a later tutorial. // For now, we will simply ray march a scene that consists of a single sphere at the origin. // We will not bother performing any fancy shading to keep things simple for now. #ifdef GL_ES precision mediump float; #endif uniform vec2 resolution; //----------------------------------------------------------------------------------------------- // The sphere function takes in a point along the ray // we are marching and a radius. The sphere function // will then return the distance from the input point p // to the closest point on the sphere. The sphere is assumed // to be centered on the origin which is (0,0,0). float sphere( vec3 p, float radius ) { return length( p ) - radius; } //----------------------------------------------------------------------------------------------- // The map function is the function that defines our scene. // Here we can define the relationship between various objects // in our scene. To keep things simple for now, we only have a single // sphere in our scene. float map( vec3 p ) { return sphere( p, 3.0 ); } //----------------------------------------------------------------------------------------------- // This function will return the normal of any point in the scene. // This function is pretty expensive so if you need the normal, you should // call this function once and store the result. Essentially the way it works // is by offsetting the input point "p" along each axis and then determining the // change is distance at each new point along each axis. vec3 getNormal( vec3 p ) { vec3 e = vec3( 0.001, 0.00, 0.00 ); float deltaX = map( p + e.xyy ) - map( p - e.xyy ); float deltaY = map( p + e.yxy ) - map( p - e.yxy ); float deltaZ = map( p + e.yyx ) - map( p - e.yyx ); return normalize( vec3( deltaX, deltaY, deltaZ ) ); } //----------------------------------------------------------------------------------------------- // The trace function is our integration function. // Given a starting point and a direction, the trace // function will return the distance from a point on the ray // to the closest point on an object in the scene. In order for // the trace function to work properly, we need functions that // describe how to calculate the distance from a point to a point // on a geometric object. In this example, we have a sphere function // which tells us the distance from a point to a point on the sphere. float trace( vec3 origin, vec3 direction, out vec3 p ) { float totalDistanceTraveled = 0.0; // When ray marching, you need to determine how many times you // want to step along your ray. The more steps you take, the better // image quality you will have however it will also take longer to render. // 32 steps is a pretty decent number. You can play with step count in // other ray marchign examples to get an intuitive feel for how this // will affect your final image render. for( int i=0; i <32; ++i) { // Here we march along our ray and store the new point // on the ray in the "p" variable. p = origin + direction * totalDistanceTraveled; // "distanceFromPointOnRayToClosestObjectInScene" is the // distance traveled from our current position along // our ray to the closest point on any object // in our scene. Remember that we use "totalDistanceTraveled" // to calculate the new point along our ray. We could just // increment the "totalDistanceTraveled" by some fixed amount. // However we can improve the performance of our shader by // incrementing the "totalDistanceTraveled" by the distance // returned by our map function. This works because our map function // simply returns the distance from some arbitrary point "p" to the closest // point on any geometric object in our scene. We know we are probably about // to intersect with an object in the scene if the resulting distance is very small. float distanceFromPointOnRayToClosestObjectInScene = map( p ); totalDistanceTraveled += distanceFromPointOnRayToClosestObjectInScene; // If our last step was very small, that means we are probably very close to // intersecting an object in our scene. Therefore we can improve our performance // by just pretending that we hit the object and exiting early. if( distanceFromPointOnRayToClosestObjectInScene < 0.0001 ) { break; } // If on the other hand our totalDistanceTraveled is a really huge distance, // we are probably marching along a ray pointing to empty space. Again, // to improve performance, we should just exit early. We really only want // the trace function to tell us how far we have to march along our ray // to intersect with some geometry. In this case we won't intersect with any // geometry so we will set our totalDistanceTraveled to 0.00. if( totalDistanceTraveled > 10000.0 ) { totalDistanceTraveled = 0.0000; break; } } return totalDistanceTraveled; } //----------------------------------------------------------------------------------------------- // Standard Blinn lighting model. // This model computes the diffuse and specular components of the final surface color. vec3 calculateLighting(vec3 pointOnSurface, vec3 surfaceNormal, vec3 lightPosition, vec3 cameraPosition) { vec3 fromPointToLight = normalize(lightPosition - pointOnSurface); float diffuseStrength = clamp( dot( surfaceNormal, fromPointToLight ), 0.0, 1.0 ); vec3 diffuseColor = diffuseStrength * vec3( 1.0, 0.0, 0.0 ); vec3 reflectedLightVector = normalize( reflect( -fromPointToLight, surfaceNormal ) ); vec3 fromPointToCamera = normalize( cameraPosition - pointOnSurface ); float specularStrength = pow( clamp( dot(reflectedLightVector, fromPointToCamera), 0.0, 1.0 ), 10.0 ); // Ensure that there is no specular lighting when there is no diffuse lighting. specularStrength = min( diffuseStrength, specularStrength ); vec3 specularColor = specularStrength * vec3( 1.0 ); vec3 finalColor = diffuseColor + specularColor; return finalColor; } //----------------------------------------------------------------------------------------------- // This is where everything starts! void main( void ) { // gl_FragCoord.xy is the coordinate of the current pixel being rendered. // It is in screen space. For example if you resolution is 800x600, gl_FragCoord.xy // could be (300,400). By dividing the fragcoord by the resolution, we get normalized // coordinates between 0.0 and 1.0. I would like to work in a -1.0 to 1.0 space // so I multiply the result by 2.0 and subtract 1.0 from it. // if (gl_FragCoord.xy / resolution.xy) equals 0.0, then 0.0 * 2.0 - 1.0 = -1.0 // if (gl_FragCoord.xy / resolution.xy) equals 1.0, then 1.0 * 2.0 - 1.0 = 1.0 vec2 uv = ( gl_FragCoord.xy / resolution.xy ) * 2.0 - 1.0; // I am assuming you have more pixels horizontally than vertically so I am multiplying // the x coordinate by the aspect ratio. This means that the magnitude of x coordinate will probably // be larger than 1.0. This allows our image to not look squashed. uv.x *= resolution.x / resolution.y; // We would like to cast a ray through each pixel on the screen. // In order to use a ray, we need an origin and a direction. // The cameraPosition is where we want our camera to be positioned. Since our sphere will be // positioned at (0,0,0), I will push our camera back by -10 units so we can see the sphere. vec3 cameraPosition = vec3( 0.0, 0.0, -10.0 ); // We will need to shoot a ray from our camera's position through each pixel. To do this, // we will exploit the uv variable we calculated earlier, which describes the pixel we are // currently rendering, and make that our direction vector. vec3 cameraDirection = normalize( vec3( uv.x, uv.y, 1.0) ); // Now that we have our ray defined, we need to trace it to see how far the closest point // in our world is to this ray. We will simply shade our scene. vec3 pointOnSurface; float distanceToClosestPointInScene = trace( cameraPosition, cameraDirection, pointOnSurface ); // We will now shade the sphere if our ray intersected with it. vec3 finalColor = vec3(0.0); if( distanceToClosestPointInScene > 0.0 ) { vec3 lightPosition = vec3( 0.0, 4.5, -10.0 ); vec3 surfaceNormal = getNormal( pointOnSurface ); finalColor = calculateLighting( pointOnSurface, surfaceNormal, lightPosition, cameraPosition ); } // And voila! We are done! We should now have a sphere! =D // gl_FragColor is the final color we want to render for whatever pixel we are currently rendering. gl_FragColor = vec4( finalColor, 1.0 ); } |