Today. More realistic illumination. Capturing environment maps. Computergrafik. Environment maps as light sources. Environment maps as light sources

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1 Today More shaders Environment mapping Computergrafik Toon shading Bump mapping Shadow mapping Matthias Zwicker Universität Bern Herbst 2008 More realistic illumination In real world, at each point in scene light arrives from all directions Not just from point light sources Environment maps Capturing environment maps 360 degrees panoramic image Instead of 360 degrees panoramic image, take picture of mirror ball (light probe) Store omni-directional illumination as images Each pixel corresponds to light from a certain direction Light probes [Paul Debevec, Environment maps as light sources Simplifying assumption Assume light captured by environment map is emitted from infinitely far away Environment map consists of directional light sources Value of environment map is defined for each direction, independent of position in scene Use single environment map at each point in the scene Approximation! Environment maps as light sources How do you compute shading of a diffuse surface using an environment map? What is more expensive to compute, shading a diffuse or a specular surface? 1

2 Environment maps applications Use environment map as light source Sphere & cube maps Store incident light on sphere or on six faces of a cube Reflection mapping Global illumination [Sloan et al.] Spherical map Cube map Cube map look-up Given direction (x,y,z) Largest coordinate component determines cube map face Dividing by magnitude of largest component yields coordinates within face Reflection mapping Simulate mirror reflection Compute reflection vector at each pixel Use reflection vector to look up cube map Rendering cube map itself is optional In GLSL Use(x,y,z) direction as texture coordinates to samplercube Reflection mapping Reflection mapping in GLSL Application setup Load, bind a cube environment map glbindtexture(gl_texture_cube_map, ); glteximage2d(gl_texture_cube_map_positive_x, ); glteximage2d(gl_texture_cube_map_negative_x, ); glteximage2d(gl_texture_cube_map_positive_y, ); glenable(gl_texture_cube_map); More details in book OpenGL Shading Language by Randi Rost Reflection mapping in GLSL Vertex shader Compute viewing direction Reflection direction Use reflect function Pass reflection direction to fragment shader Fragment shader Look-up cube map using interpolated reflection direction varying float3 refl; uniform samplercube envmap; texturecube(envmap, refl); 2

3 Reflection mapping examples Approximation, reflections are not accurate Demo NVidia CG shading language Cg c7 reflection [NVidia] Today More shaders Environment mapping Toon shading Bump mapping Shadow mapping Toon shading Simple cartoon style shader Emphasize silhouettes Discrete steps for diffuse shading, highlights Off-line toon shader GLSL toon shader Toon shading Silhouette edge detection Compute dot product of viewing direction v and normal n Use 1D texture to define edge ramp uniform sample1d edgeramp; e=texture1d(edgeramp,edge); edgeramp 1 0 edge Toon shading Compute diffuse and specular shading Use 1D textures diffuseramp, specularramp to map diffuse and specular shading to colors Final color uniform sampler1d diffuseramp; uniform sampler1d specularramp; c = e * (texture1d(diffuse,diffuseramp)+ texture1d(specular,specularramp)); 3

4 Toon shading Cg toon9 More shaders OpenGL shading language book NVidia shader library Most shadersare in HLSL s/shader_library.html html NVidiaCg toolkit Predecessor of GLSL Lots of example shaders Today More shaders Environment mapping Toon shading Bump mapping Shadow mapping Bump mapping Surface detail is often the result of small perturbations in the surface geometry Modeling detailed surfaces would lead to impractical number of triangles Bump mapping alters the surface normal to provide the illusion of small scale surface detail Normals are encoded in texture maps Requires per-pixel shading using a fragment program Bump mapping Bump mapping Generating and storing bump maps Rendering with bump maps No bump mapping With bump mapping Bump mapped plane No bump mapping With bump mapping Bump texture 4

5 Generating bump maps Usually done in a pre-process Input Texture map that encodes small surface displacements Height field E.g., use gray scale image as height values Output Texture map that encodes normals of displaced surface This texture will be stored as an image, read by the application Generating bump maps Displacement map Normal Discrete case using central differencing Normalize! Storing bump maps Encode normal direction in RGB color channels Coordinates of unit normal are in [-1..1] 3 Need to map range [-1..1] to [0..255] for all channels Rendering with bump maps When applying a bump map to a curved surface, how are the normals specified in the bump map related to the surface? Normals are defined relative to local tangent/normal vectors Normals Local tangent vector RGB encoded bump map Normals in bump map Bump map applied to curved surface Rendering with bump maps Bump map normals are defined in tangent space Defined by two tangent vectors and normal Will define tangent space for each triangle Texture coordinates provide parameterization of each triangle, i.e., function Compute tangent space using partial derivatives of parameterization Will need to transform normals from tangent space to camera space Tangent space Triangle with texture coordinates can be expressed as parametric surface Triangle vertices in object space We know 5

6 Tangent space Solve for affine function Tangent space Tangent space defined by tangent, bi-tangent, and normal vectors Using correspondences at vertices defined in object space coordinates Tangent, bi-tangent not orthogonal in general No normalization necessary Normal in object space Normal map stores normals in tangent coordinates Basis vectors Can transform normal from tangent to object space Values [bm 0,bm 1,bm 2 ] from bump map Unpacked from [0..1] to range [-1..1] Storing tangent vectors Before rendering For each triangle, compute tangent, bitangent vector At each vertex, average tangent, bitangent vectors over adjacent triangles Store tangent vectors as additional vertex attributes Rendering Vertex shader Per-vertex input Vertex position, normal, tangent vector in object space Bump map texture coordinates Compute bi-tangent vector Transform everything to camera space using modelview matrix Output to fragment shader Vertex position, texture coordinates, tangent, bitangent, normal vector in camera space Bump map texture coordinates Rendering with bump maps Fragment shader Transform normal [bm 0,bm 1,bm 2 ] stored in bump map to camera coordinates Use basis to transform to object space Use modelview matrix to transform from object space to camera space Normalize Perform lighting in camera coordinates 6

7 Variations Perform lighting in different coordinate system than camera space Object space Tangent space Tangent space is more efficient Transform light direction to tangent space in vertex shader Interpolate across triangle No need to transform bump mapped normal at each pixel Caveats Avoid triangles with zero area in texture space Cannot compute valid tangent space Avoid triangles with negative area in texture space May happen when texture is mirrored Avoid non-uniform stretching of bump map Combination with env. map Environment mapped bump mapping (EMBM) Use bump mapped normal to compute reflection vector, look up cube map Demo AMD RenderMonkey Shader development IDE Supports GLSL, HLSL, etc. Illumination_Advanced.rfx Reflection_Refractions.rfx [ Env. mapped bump mapping Use additional dirt texture to modulate strength of reflection from environment map Tutorials Caution, slightly different derivation OpenGL shading language book Bump mapping uses shading p pp g g in tangent space 7

8 Today More shaders Environment mapping Toon shading Bump mapping Shadow mapping Why are shadows important? Cues on scene lighting Why are shadows important? Contact points Depth cues Why are shadows important? Realism Without self-shadowing Without self-shadowing Terminology Umbra: fully shadowed region Penumbra: partially shadowed region (area) light source occluder Hard and soft shadows Point and directional lights lead to hard shadows, no penumbra Area light sources lead to soft shadows, with penumbra point directional area penumbra umbra shadow receiver umbra penumbra 8

9 Hard and soft shadows Hard shadow, point light source Soft shadow, area light source Shadows for interactive rendering Focus on hard shadows Soft shadows often too hard to compute in interactive graphics Two main techniques Shadow mapping Shadow volumes Many variations, subtleties Active research area Shadow mapping Main idea Scene point is lit by light source if it is visible from light source Determine visibility from light source by placing camera at light source position and rendering scene Two pass algorithm First pass Render scene by placing camera at light source position Store depth image (shadow map) depth value Scene points are lit if visible from light source Determine visibility from light source by placing camera at light source position Depth image seen from light source Two pass algorithm Second pass Render scene from camera position At each pixel, compare distance to light source with value in shadow map If distance is larger, we are in shadow If distance is smaller or equal, pixel is lit v b is in shadow Final image with shadows pixel seen from eye v b Demo Cg tutorial examples shadowmapping 9

10 Issues Limited field of view of shadow map Z-fighting Sampling problems Limited field of view What if a scene point is outside the field of view of the shadow map? field of view Limited field of view z-fighting What if a scene point is outside the field of view of the shadow map? Use six shadow maps, arranged in a cube Requires rendering pass for each shadow map! shadow maps Depth values for points visible from light source are equal in both rendering passes Because of limited resolution, depth of pixel visible from light could be larger than shadow map value Need to add bias in first pass to make sure pixels are lit Shadow map Shadow map pixels Depth of shadow map Camera image Image pixels Pixel is considered in shadow! Depth of pixel Solution Add bias when rendering shadow map Move geometry away from light by small amount Finding correct amount of bias is tricky Bias Not enough Too much Correct bias Not enough bias Too much bias Correct 10

11 Sampling problems Shadow map pixel may project to many image pixels Ugly stair-stepping artifacts Solutions Increase resolution of shadow map Not always sufficient Split shadow map into several slices Tweak projection for shadow map rendering Light space perspective shadow maps (LiSPSM) With GLSL source code! Combination of splitting and LiSPSM Basis for most serious implementations LiSPSM Percentage closer filtering Instead of looking up one shadow map pixel, look up several pixels Perform depth test for each shadow map pixel Compute percentage of pixels that are lit Basic shadow map Light space perspective shadow map Percentage closer filtering Supported in hardware for small filters (2x2 shadow map pixels) Next time Advanced topics Can use larger filters with additional rendering passes Fake soft shadows 11

12 Appendix Shadow mapping with OpenGL Recommended book: OpenGL Shading Language by Randi Rost First pass Render scene by placing camera at light source position Compute light view (look at) matrix Similar to computing camera matrix from look-at, up vector Compute its inverse to get world-to-light transform Determine view frustum such that scene is completely enclosed Use several view frusta/shadow maps if necessary First pass Each vertex point is transformed by Object-to-world (modeling) matrix World-to-light li space matrix Light frustum (projection) matrix Remember: points within frustum are transformed to unit cube [-1,1] 3 Object space (1,1) Light space (-1,-1) First pass Use glpolygonoffset to apply depth bias Store depth image in a texture Use glcopyteximage with internal format GL_DEPTH_COMPONENT Final result with shadows Scene rendered from light source Depth map from light source Second pass Render scene from camera At each pixel, look up corresponding location in shadow map Compare depths with respect to light source Looking up shadow map Need to transform each point from object space to shadow map Shadow map texture coordinates are in [0,1] 2 Transformation from object to shadow map coordinates (set it as texture matrix, see below) (1,1) After perspective projection we have shadow map coordinates (0,0) Object space Light space Shadow map 12

13 Looking up shadow map Transform each vertex to normalized frustum of light Pass s,t,r,q as texture coordinates to rasterizer Rasterizer interpolates s,t,r,q to each pixel Use projective texturing to look up shadow map This means, the texturing unit automatically computes s/q,t/q,r/q,1 s/q,t/q are shadow map coordinates in [0,1] 2 r/qis depth in light space Shadow depth test: compare shadow map at (s/q,t/q) to r/q GLSL specifics In application Store matrix T in OpenGL texture matrix Set usingglmatrixmode(gl_texture) In vertex shader Access texture matrix through predefined uniform gl_texturematrix In fragment shader Declare shadow map as sampler2dshadow Look up shadow map using projective texturing with vec4 texture2dproj(sampler2d, vec4) GLSL specifics When you do a projective texture look up on a sampler2dshadow, the depth test is performed automatically Return value is (1,1,1,1) if lit Return value is (0001)if (0,0,0,1) shadowed Simply multiply result of shading with current light source with this value Resources Overview, lots of links Basic shadow maps Avoiding sampling problems in shadow maps p p Faking soft shadows with shadow maps Alternative: shadow volumes