11/24/ :45 Graphics II Shadow Maps Reflections Session 5

21/24/ :45 Shadow Maps Eye Point Light Source Objects

31/24/ :45 Shadow Maps: The algorithm 1. Transform the scene objects to the light source coordinates (x’,y’,z’). 2. Disable color buffer writing and render the scene objects into the z - buffer 3. Copy this buffer into a “shadow z - buffer” 4. Transform the scene back to the eye coordinates (x,y,z). 5. Render the scene. At each pixel, if a point on a surface is deemed to be visible, it is transformed into light source coordinates: (x,y,z) -> (x’,y’,z’). The x’ and y’ coordinates are used to index into the shadow z-buffer and z’ is compared with the z value in the buffer. If z’ is greater than this value, the point is in shadow and it is rendered as if the light is turned off. 6. Repeat for other light sources, and accumulate color

41/24/ :45 Shadow Maps Tradeoffs 0 Excellent for situations when shadowing and shadowed objects are both complex 0 Some graphics systems do not provide necessary primitives or buffers 0 Aliasing is a problem -Possible solutions =Use high - resolution shadow z buffer =Jitter shadow texture to smooth out edges 0 Difficult to find appropriate projection when light source is in the middle of scene objects

51/24/ :45 Finite light sources produce “soft shadows” Finite size light source Shadowing object

61/24/ :45 Simulating finite size light source by Multiple point sources: “dithering” Light source moves in grid Shadowing Object (polygon) Plane of projection Shadows are “accumulated”

71/24/ :45 The Accumulation Buffer Color Planes Accumulation Buffer Color data

81/24/ :45 Accumulation buffer use: void glAccum(glenum op,glFloat value); op: GL_ACCUM reads each pixel from buffer currently selected for reading and multiplies RGBA values by value and adds the result to accumulation buffer. GL_LOAD reads each pixel from the buffer currently selected for reading, multiplies RGBA values by value and replaces values in accumulation buffer. GL_RETURN takes values from the accumulation buffer, mutiplies them by value, and places them in the color buffer. GL_ADD, GL_MULT adds or multiplies the value of each pixel in the accumulation buffer by value and returns it to the accumulation buffer.

91/24/ :45 Accumulation Buffer op = GL_ACCUM Value X  Color Planes Accumulation Buffer

101/24/ :45 Accumulation Buffer op = GL_LOAD Value X Color Planes Accumulation Buffer

111/24/ :45 Accumulation Buffer op = GL_RETURN Value X Color Planes Accumulation Buffer

121/24/ :45 Accumulation Buffer op = GL_MULT Value X Accumulation Buffer

131/24/ :45 Projection Shadows Code example. 120 goto 240

141/24/ :45 Reflections Direct ray Reflected ray Eye point Plane of Reflection

151/24/ :45 Reflection Transformations: across major planes of symmetry Y- Z PlaneX - Z PlaneX - Y Plane

161/24/ :45 Reflection transformations: the general case X - Z plane Arbitrary plane

171/24/ :45 Reflection Transformations: the general case - constructing the transformation Inverse transformationReflection across X - Z Plane Transformation to move reflecting plane to X - Z plane

181/24/ :45 Reflections: Visibility Issues Finite Size Reflecting Object Eyepoint Real Cone Real Ball Reflected Cone Reflected Ball Not Visible

191/24/ :45 Reflections: Visibility Issues Finite Size Reflecting Object Eyepoint Real Cone Should be obstructed by reflecting object “Reflected Cone” Should not be visible

201/24/ :45 Solution to visibility issues: use stencil and z buffer The algorithm: 1. Disable the depth test 2. Set stencil operation to replace with 1 3. Draw the reflecting polygon 4. Set the stencil operation to only draw where stencil=1 5. Multiply reflecting transformation onto modelview matrix 6. Enable depth test, render objects. Clip objects that are on opposite side of the reflecting plane from eyepoint. 7. Disable stencil test 8. Remove reflection transformation from modelview 9. Disable writing to color buffer 10. Draw the reflecting polygon 11. Enable writing to color buffer 12. Render the scene (unreflected)

211/24/ :45 Projection Shadows Code example. 120 goto 240

221/24/ :45 Rendered with Ray Tracing

231/24/ :45 Arbitrarily shaped reflective object. Eye point

241/24/ :45 Sphere Map

251/24/ :45

261/24/ :45 Calculation of Texture Coordinates For each vertex, the reflected vector direction is given by: Let m be defined as: The texture coordinates are given by:

271/24/ :45 Sphere Mapping: The OpenGL Algorithm 1. Bind the texture containing the sphere map. 2. Set sphere mapping texture coordinate generation: glTexGen(GL_S, GL_TEXTURE_GEN_MODE, GL_SPHERE_MAP); glTexGen(GL_T, GL_TEXTURE_GEN_MODE, GL_SPHERE_MAP); 3. Enable texture coordinate generation: glEnable(TEXTURE_GEN_S) 4. Draw the object, providing correct normals on a per- face or per-vertex basis.

281/24/ :45 Obtaining the Sphere Map Manually Camera Reflective Sphere at object location

291/24/ :45 Generating a Sphere Map: Image Cube Algorithm

301/24/ :45 Four of the six cube environment projections

311/24/ :45 Sphere map generated by Image cube faces