**URL**: http://glslsandbox.com/e#29767.1

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// Ray Marching Tutorial // 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 ); } //----------------------------------------------------------------------------------------------- // 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 ) { 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. vec3 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 = 0.0; break; } } return totalDistanceTraveled; } //----------------------------------------------------------------------------------------------- // 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 ); |