11 - Bump Mapping. Bump-Mapped Objects. Bump-Mapped Objects. Bump-Mapped Objects. Limitations Of Texture Mapping. Bumps: Perturbed Normals
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1 CSc 155 Advanced Compter Graphics Limitations Of extre Mapping extre mapping paints srfaces o extre image is typically fixed Some characteristics are difficlt to textre o Roghness, Wrinkles extre illmination direction is fixed o extre looks wrong if scene lighting changes In smmary, it doesn t take into accont how lighting wold be deflected off of the textre 2 Bmps: Pertrbed ormals Bmp-Mapped Objects Srface normals on a real bmp Srface normals on a flat polygon Modified ( pertrbed ) normals 3 4 Bmp-Mapped Objects Bmp-Mapped Objects 5 6
2 Obtaining Bmp Fnctions Explicit Bmp Fnctions Original parametric srface Bmp fnction b( sin( π Modified bmpy srface 7 8 Compting Pertrbed ormals ew srface points are implied by and b( Implied bmpy srface ) ˆ P( P( P( ˆ * b( Approximating the normal at new srface point: Bmp fnction b( P( ˆ P( P( P( ˆ * b( slope of b( ˆ d b( d d b d A good approximation for the new normal is [Blinn] 9 10 Relationship of bmp fnction slope to modified normals: positive slope Bmp fnction b( slope = negative slope Similar steps apply for 3D srfaces: Srface implied by Bmp fnction b( v P( P P( ( B slope indirection B P( B slope invdirection v P( P( ˆ b( Vectors in local ( tangent ) space 11 12
3 v Approximating : P( ˆ P( B B ˆ v b( b( ˆ B ˆ P( P( ˆ b( P( P( ˆ b( B v v v B Smmary ( procedral bmp mapping ) o Given a parametric srface P(, o the existing normal at ( can be pertrbed in each of two directions and v o by adding small changes Δ and Δv respectively o where Δ and Δv are derived from the slope of a bmp fnction, b(. o he new normal is then sed in the lighting and shading eqations. Bmp fnction slope in v Vector in B direction Bmp fnction slope in Vector in direction ormal Mapping Encoding ormals In RGB Basic bmp-mapping goal: alter the normal Alternative: replace normals o eed a sorce of new normals ormals (when normalied) are nit length o hence, (x*x)+(y*y)+(*) = 1, and therefore -1 <= x,y, <= 1 ew normals can be stored in 3 bytes (e.g. in a color image): r = (x+1)/2 g = (y+1)/2 b = (+1)/2 A tre nit normal is perpendiclar to the srface (has vale [0 0 1]) o eed to represent Δx/Δy deviations (positive or negative) RGB vales can range from o Choose midrange R & G vales to represent Δx = Δy = 0 ˆ R G B Z As ints: Y As floats: Δx=0 Δy= A ormal Map image file Diffsely lit textred tors Generating ormal Maps meros software packages are available: GIMP Photoshop plgins SS_Bmp_Generator etc. ormal-mapped tors Image credit: Pal Baker,
4 Lighting Calclations angent Space L H V B L Problem: vectors freqently not in same space o ormal, Light, angent, Bitangent, eye, etc. Soltion: transform vectors to common local or tangent space eeded: Light vector in angent Space, for each vertex x Bx B x 0 B y 0 y y B Using B vales he B matrix doesn t sally have to be bilt, becase the comptations redce to: lightdir = vec3 ( (L ), (L B), (L ) ) eyedir = vec3 ( (V ), (V B), (V ) ) he binormal vector (B) is easily compted by x Storing B vales Mst be compted/saved per vertex Vertex3D... - normal : Vector3D - tangent : Vector3D - binormal : Vector3D - tangentspacelight : Vector3D... hs, the application only needs to obtain and. 21 graphicslib3d Vertex3D class has fields for storing the relevant vales, bt application code needs to provide them. 22 Y ors With B Vales Oter Radis B B Z Precision Ring 0 Inner Radis Precision Inner Radis Oter Radis Front View Y op View 23 angent Space In Shaders Application code: o Provide vertex tangent and normal vectors Vertex shader: o Use vertex tangent and normal to bild Binormal (B) vector o Use B to convert light and view vectors to tangent space o Compte vertex position sing ModelViewProjection matrix o Send to fragment processor: vertex position textre coordinates L and V in tangent space Fragment shader (two approaches): H L V o Procedral bmp fnction in fragment shader (seen previosly) o Get bmps / normals from a textre nit sing a sampler variable 24
5 Height Mapping A monochrome image where pixel intensity = height Low vales (black) = low height High vales (white) = high height Interpretation: Original Height Field Image Height Field Image 25 Edge-on (tilted) View 26 Expanded Portion Height Maps for lighting We can se the difference between adjacent pixels as an approximation of the slope Height map lighting example Pixel vale: Forward Diffs: A bmp map height field textre file A checker-board textred bmp-mapped cylinder Height Maps for altering position We can se the brightness of a texel to alter the actal y-coordinate of a position P.y = P.y P.y = P.y P.y = P.y example: height map in vertex shader #version 430 layot (location=0) in vec4 vertpos; layot (location=1) in vec2 tex_coord;... layot (binding=0) niform sampler2d s; layot (binding=1) niform sampler2d t;... void main(void) { vec4 P = vertpos; P.y = P.y + textre2d(s,tex_coord).r; P = mv_matrix * P;... } tc = tex_coord; gl_position = proj_matrix * P; // the vertex geometric position // textre coordinates // height map // textre image 30
6 height map in vertex shader (cont.) height map (textre 1) Limitations Vertex shaders are limited to vertices Height vales between vertices are interpolated, rather than looked p in the height map Details in the height map can therefore be lost. color map (textre 2) applied to a tors We need a way to modify locations in between the original model vertices. Later we will achieve this in the tessellation shader
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