Reading. 13. Texture Mapping. Non-parametric texture mapping. Texture mapping. Required. Watt, intro to Chapter 8 and intros to 8.1, 8.4, 8.6, 8.8.

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1 Reading Reqired Watt, intro to Chapter 8 and intros to 8.1, 8.4, 8.6, 8.8. Recommended 13. Textre Mapping Pal S. Heckbert. Srvey of textre mapping. IEEE Compter Graphics and Applications 6(11): , November Optional Watt, the rest of Chapter 8 Woo, Neider, & Davis, Chapter 9 James F. Blinn and Martin E. Newell. Textre and reflection in compter generated images. Commnications of the ACM 19(10): , October Textre mapping Non-parametric textre mapping With non-parametric textre mapping : Textre mapping (Woo et al., fig. 9-1) Textre mapping allows yo to take a simple polygon and give it the appearance of something mch more complex. Textre size and orientation are fixed They are nrelated to size and orientation of polygon Gives cookie-ctter effect De to Ed Catmll, PhD thesis, 1974 Refined by Blinn & Newell, 1976 Textre mapping ensres that all the right things happen as a textred polygon is transformed and rendered. 3 4

2 Parametric textre mapping Implementing textre mapping A textre lives in it own image coordinates paramaterized by (,v) in the range ([0..1], [0..1]): v It can be wrapped arond many different srfaces: With parametric textre mapping, textre size and orientation are tied to the polygon. Idea: Separate textre space and screen space Textre the polygon as before, bt in textre space Deform (render) the textred polygon into screen space = x/w = φ/2π = φ/2π v = θ/π A textre can modlate jst abot any parameter diffse color, speclar color, speclar exponent, Compting (,v) textre coordinates in a ray tracer is fairly straightforward. Note: if the srface moves/deforms, the textre goes with it. 5 6 Textre resampling The textre is sally stored as an image. Q: What do yo do when the textre sample yo need lands between textre pixels? Ray intersection Mapping to textre pixels Close-p Where: (y 0, φ 0 ) v 0 0 = φ/2π (, v ) = ( i + a, j + b ) 0 0 =1/ x =1/ y w h y x x y y tex tex x ( 0, v 0 ) Textre resampling To get the in between vales, we need to resample the textre. (y 0, φ 0 ) v 0 = φ/2π Ray intersection Mapping to textre pixels Close-p A common choice is bilinear resampling: 0 y x ( x x y y) T(, v ) = T i + a, j + b 0 0 = T[ i, j] + T[ i+ 1, j] + ( 0, v 0 ) T[ i, j+ 1] + T[ i+ 1, j+ 1] 7 8

3 Textre mapping and the z-bffer Solid textres Textre-mapping can also be handled in z-bffer algorithms. Method: Q: What kinds of artifacts might yo see from sing a marble veneer instead of real marble? y Scan conversion is done in screen space, as sal Each pixel is colored according to the textre Textre coordinates are fond by Gorad-style interpolation z One soltion is to se solid textres: x Use model-space coordinates to index into a 3D textre Like carving the object from the material One difficlty of solid textring is coming p with the textres. Note: Mapping is more complicated if yo want to do perspective right! 9 10 Solid textres (cont'd) Displacement mapping Here's an example for a vase ct from a solid marble textre: Textres can be sed for more than jst color. In displacement mapping, a textre is sed to pertrb the srface geometry itself: Q() N() = normal[q()] Q() = Q() + d()n() d() These displacements animate with the srface Solid marble textre by Ken Perlin, (Foley, IV-21) Q: Do yo have to do hidden srface calclations on Q? 11 12

4 Bmp mapping Displacement vs. bmp mapping In bmp mapping, a textre is sed to pertrb the normal: Inpt textre Use the original, simpler geometry, Q(), for hidden srfaces Use the normal from the displacement map for shading: N = normal[q()] Rendered as displacement map over a rectanglar srface Q() Q: What artifacts in the images wold reveal that bmp mapping is a fake? Displacement vs. bmp mapping (cont'd) Environment mapping In environment mapping (also known as reflection mapping), a textre is sed to model an object's environment: Original rendering Rendering with bmp map wrapped arond a cylinder Bmp map and rendering by Wyvern Aldinger Rays are bonced off objects into environment Color of the environment sed to determine color of the illmination Really, a simplified form of ray tracing Environment mapping works well when there is jst a single object or in conjnction with ray tracing Under simplifying assmptions, environment mapping can be implemented in hardware. With a ray tracer, the concept is easily extended to handle refraction as well as reflection

5 Combining textre maps Combining textre maps (cont'd) Using textre maps in combination gives even better effects, as Yong Sherlock Holmes demonstrated Environment- mapped mirror reflection Phong lighting with diffse textre Bmp mapping + Glossy reflection Combine textres and add dirt Constrction of the glass knight, (Foley, IV-24) Rivet stains + Shinier reflections Close-p Constrction of the glass knight, (Foley, IV-24) Antialiasing Compting the average color If yo point-sample the textre map, yo get aliasing: The comptationally difficlt part is smming over the covered pixels. Several methods have been sed: The simplest is brte force: Figre ot which texels are covered and add p their colors to compte the average. From Crow, SIGGRAPH '84 Proper antialiasing reqires area averaging in the textre: From Crow, SIGGRAPH '

6 Mip maps Mip map pyramid T 4 T 3 128x128 64x x1 T 2 T 1 magnify T 0 The mip map hierarchy can be thoght of as an image pyramid: A faster method is mip maps developed by Lance Williams in 1983: Stands for mltm in parvo many things in a small place Keep textres prefiltered at mltiple resoltions Has become the graphics hardware standard Level 0 (T 0 [i,j]) is the original image. Level 1 (T 1 [i,j]) averages over 2x2 neighborhoods of original. Level 2 (T 2 [i,j]) averages over 4x4 neighborhoods of original Level 3 (T 3 [i,j]) averages over 8x8 neighborhoods of original What s a fast way to pre-compte the textre map for each level? Mip map resampling Smmed area tables Filter size 8x8 5x5 4x4 v v T 2 ( 0, v 0 ) T 1 A more accrate method than mip maps is smmed area tables invented by Frank Crow in Recall from calcls: b b a f( xdx ) = f( xdx ) f( xdx ) a What wold the mip-map retrn for an average over a 5x5 neighborhood at location ( 0,v 0 )? How do we measre the fractional distance between levels? What if yo need to average over a non-sqare region? In discrete form: m m k f[] i= f[] i f[] i i= k i= 0 i= 0 Q: If we wanted to do this real fast, what might we pre-compte? 23 24

7 Smmed area tables (cont d) Comparison of techniqes We can extend this idea to 2D by creating a table, S[i,j], that contains the sm of everything below and to the left. Point sampled S[i, j] t MIP-mapped b l r Smmed area table Q: How do we compte the average over a region from (l, b) to (r, t)? From Crow, SIGGRAPH '84 Characteristics: Reqires more memory Gives less blrry textres Smmary What to take home from this lectre: 1. The meaning of the boldfaced terms. 2. Familiarity with the varios kinds of textre mapping, inclding their strengths and limitations. 3. Understanding of the varios approaches to antialiased textre mapping: Brte force Mip maps Smmed area tables 27