Texture Mapping. Most slides courtesy of Leonard McMillan and Jovan Popovic

Size: px

Start display at page:

Download "Texture Mapping. Most slides courtesy of Leonard McMillan and Jovan Popovic"

Calvin Kelly
5 years ago
Views:

1 Texture Mapping Why texture map? How to do it How to do it right Spilling the beans A couple tricks Difficulties with texture mapping Projectie mapping Shadow mapping Enironment mapping Most slides courtesy of Leonard McMillan and Joan Popoic Lecture 15 Slide Fall 2002

2 Administratie Office hours Durand & Teller by appointment gan Thursday 4-7 in W Yu Friday 2-5 in E Deadline for proposal: Friday o 1 Meeting with faculty & staff about proposal ext week Web page for appointment Lecture 15 Slide Fall 2002

3 The Quest for Visual Realism For more info on the computer artwork of Jeremy Birn see Lecture 15 Slide Fall 2002

4 Photo-textures The concept is ery simple! Lecture 15 Slide Fall 2002

Texture Coordinates Specify a texture coordinate at each ertex (s, t) or (u, ) Canonical coordinates where u and are between 0 and 1 Simple modifications to triangle rasterizer (0,1) (0,0) (1,0) Void

5 Texture Coordinates Specify a texture coordinate at each ertex (s, t) or (u, ) Canonical coordinates where u and are between 0 and 1 Simple modifications to triangle rasterizer (0,1) (0,0) (1,0) Void EdgeRec::init() { //ote: here we use w=1/z wstart=1./z1; wend=1./z2; dw=wend-wstart; wcurr=wstart; sstart=s1; send=s2; ds=sstart-send; scurr=sstart; tstart=t1; tend=t2; dt=tstart-tend; tcurr=tstart; } Void EdgeRec::update () { ycurr+=1; xcurr+=dx; wcurr+=dw; scurr+=ds; tcurr+=dt; } static oid RenderScanLine ( ) { for (e1 = AEL->ToFront(); e1!= ULL; e1 = AEL->ext() ) { e2=ael->extpolyedge(e1->poly); x1=[e1->xcurr]; x2=[e2->xcurr]; dx=x2-x1; w1=e1->wcurr; w2=e2->wcurr; dw=(w2-w1)/dx; s1=e1->scurr; s2=e2->scurr; ds=(s2-s1)/dx; t1=e1->tcurr; t2=e2->tcurr; dt=(t2-t1)/dx; for (int x=x1; x<x2; x++) { w+=dw; s+=ds; t+=dt; if (w<wbuffer[x]) { wbuffer[x]=w; raster.setpixel(x, texturemap[s,t]) } } } raster->write(y); } Lecture 15 Slide Fall 2002

6 The Result Let's try that out... Texture mapping applet (image) Wait a minute... that doesn't look right. What's going on here? Let's try again with a simpler texture... Texture mapping applet (simple texture) otice how the texture seems to bend and warp along the diagonal triangle edges. Let's take a closer look at what is going on. Lecture 15 Slide Fall 2002

7 Looking at One Edge First, let's consider one edge from a gien triangle. This edge and its projection onto our iewport lie in a single common plane. For the moment, let's look only at that plane, which is illustrated below: Lecture 15 Slide Fall 2002

8 Visualizing the Problem otice that uniform steps on the image plane do not correspond to uniform steps along the edge. Let's assume that the iewport is located 1 unit away from the center of projection. Lecture 15 Slide Fall 2002

9 Linear Interpolation in Screen Space Compare linear interpolation in screen space Lecture 15 Slide Fall 2002

10 Linear Interpolation in 3-Space to interpolation in 3-space Lecture 15 Slide Fall 2002

11 How to Make Them Mesh Still need to scan conert in screen space... so we need a mapping from t alues to s alues. We know that the all points on the 3-space edge project onto our screenspace line. Thus we can set up the following equality: and sole for s in terms of t giing: Unfortunately, at this point in the pipeline (after projection) we no longer hae z 1 lingering around (Why?). Howeer, we do hae w 1 = 1/z 1 and w 2 = 1/z 2. Lecture 15 Slide Fall 2002

12 Interpolating Parameters We can now use this expression for s to interpolate arbitrary parameters, such as texture indices (u, ), oer our 3-space triangle. This is accomplished by substituting our solution for s gien t into the parameter interpolation. Therefore, if we premultiply all parameters that we wish to interpolate in 3-space by their corresponding w alue and add a new plane equation to interpolate the w alues themseles, we can interpolate the numerators and denominator in screen-space. We then need to perform a diide a each step to get to map the screen-space interpolants to their corresponding 3-space alues. Once more, this is a simple modification to our existing triangle rasterizer. Lecture 15 Slide Fall 2002

13 Modified Rasterizer Void EdgeRec::init() { wstart=1./z1; wend=1./z2; dw=wend-wstart; wcurr=wstart; swstart=s1*w1; swend=s2*w2; dsw=swstart-swend; swcurr=swstart; twstart=t1*w1; twend=t2*w2; dtw=twstart-twend; twcurr=twstart; } Void EdgeRec::update () { ycurr+=1; xcurr+=dx; wcurr+=dw; swcurr+=dsw; twcurr+=dtw; } static oid RenderScanLine ( ) { for (e1 = AEL->ToFront(); e1!= ULL; e1 = AEL->ext() ) { e2=ael->extpolyedge(e1->poly); x1=[e1->xcurr]; x2=[e2->xcurr]; dx=x2-x1; w1=e1->wcurr; w2=e2->wcurr; dw=(w2-w1)/dx; sw1=e1->swcurr; sw2=e2->swcurr; dsw=(sw2-sw1)/dx; tw1=e1->twcurr; tw2=e2->twcurr; dtw=(tw2-tw1)/dx; for (int x=x1; x<x2; x++) { w+=dw; float denom = 1.0f / w; sw+=dsw; tw+=dtw; correct_s=sw*denom; correct_t=tw*denom; if (w<wbuffer[x]) { wbuffer[x]=w; raster.setpixel(x, texturemap[correct_s, correct_t]) } } } raster->write(y); } Lecture 15 Slide Fall 2002

14 Demonstration For obious reasons this method of interpolation is called perspectiecorrect interpolation. The fact is, the name could be shortened to simply correct interpolation. You should be aware that not all 3-D graphics APIs implement perspectie-correct interpolation. Applet with correct interpolation You can reduce the perceied artifacts of non-perspectie correct interpolation by subdiiding the texture-mapped triangles into smaller triangles (why does this work?). But, fundamentally the screen-space interpolation of projected parameters is inherently flawed. Applet with subdiided triangles Lecture 15 Slide Fall 2002

15 Reminds you something? When we did Gouraud shading didn't we interpolate illumination alues, that we found at each ertex using screenspace interpolation? Didn't I just say that screen-space interpolation is wrong (I beliee "inherently flawed" were my exact words)? Does that mean that Gouraud shading is wrong? Lecture 15 Slide Fall 2002

16 Gouraud is a big simplification Gourand shading is wrong. Howeer, you usually will not notice because the transition in colors is ery smooth (And we don't know what the right color should be anyway, all we care about is a pretty picture). There are some cases where the errors in Gouraud shading become obious. When switching between different leels-of-detail representations At "T" joints. Applet showing errors in Gouraud shading Lecture 15 Slide Fall 2002

17 Texture Tiling Often it is useful to repeat or tile a texture oer the surface of a polygon. if (w<wbuffer[x]) { wbuffer[x]=w; raster.setpixel(x, texturemap[tile(correct_s, max), tile(correct_t, max)]) } int tile(int al, int size) { if (al >= size) { do { al -= size; } while (al >= size); } else { while (al < 0) { al += size; } } return al; } Tiling applet Can also use symmetries Lecture 15 Slide Fall 2002

18 Texture Transparency There was also a little code snippet to handle texture transparency. if (w<wbuffer[x]) { Color4=raster.setPixel(x, oldcolor=raster.getpixel(x); texturecolor= texturemap[tile(correct_s, max), tile(correct_t, max)]; float t= texturecolor.transparency() newcolor = t*texturecolor+ (1-t)*oldColor; raster.setpixel(x, newcolor) wbuffer[x]=w; //OT SO SIMPLE.. BEYOD THE SCOPE OF THIS LECTURE } Applet showing texture transparency Lecture 15 Slide Fall 2002

Summary of Label Textures Increases the apparent complexity of simple geometry Must specify texture coordinates for each ertex Projectie correction (can't linearly interpolate in screen space)

19 Summary of Label Textures Increases the apparent complexity of simple geometry Must specify texture coordinates for each ertex Projectie correction (can't linearly interpolate in screen space) Specify ariations in shading within a primitie Two aspects of shading Illumination Surface Reflectace Label textures can handle both kinds of shading effects but it gets tedious Acquiring label textures is surprisingly tough Lecture 15 Slide Fall 2002

Difficulties with Label Textures Tedious to specfiy texture coordinates for eery triangle Textures are attached to the geometry Easier to model ariations in reflectance than illumination Can't use

20 Difficulties with Label Textures Tedious to specfiy texture coordinates for eery triangle Textures are attached to the geometry Easier to model ariations in reflectance than illumination Can't use just any image as a label texture The "texture" can't hae projectie distortions Reminder: linear interploation in image space is not equialent to linear interpolation in 3- space (This is why we need "perspectiecorrect" texturing). The conerse is also true. Textures are attached to the geometry Easier to model ariations in reflectance than illumination Makes it hard to use pictures as textures Lecture 15 Slide Fall 2002

21 Projectie Textures Treat the texture as a light source (like a slide projector) o need to specify texture coordinates explicitly A good model for shading ariations due to illumination A fair model for reflectance (can use pictures) Lecture 15 Slide Fall 2002

22 Projectie Textures texture Projected onto the interior of a cube [Segal et al. 1992] Lecture 15 Slide Fall 2002

The Mapping Process During the Illumination process: For each ertex of triangle (in world or lighting space) Compute ray from the projectie texture's origin to point Compute homogeneous texture

23 The Mapping Process During the Illumination process: For each ertex of triangle (in world or lighting space) Compute ray from the projectie texture's origin to point Compute homogeneous texture coordinate, [ti, tj, t] (use projectie matrix) During scan conersion (in projected screen space) Interpolate all three texture coordinates in 3-space (premultiply by w of ertex) Do normalization at each rendered pixel i = t i / t j = t j / t Access projected texture Lecture 15 Slide Fall 2002

24 Projectie Texture Examples Modeling from photograph Using input photos as textures [Debeec et al. 1996] Lecture 15 Slide Fall 2002

We can simply use the texture as the final color for the pixel, or we can just use it as diffuse color, or we can use

25 Adding Texture Mapping to Illumination Texture mapping can be used to alter some or all of the constants in the illumination equation. We can simply use the texture as the final color for the pixel, or we can just use it as diffuse color, or we can use the texture to alter the normal, or... the possibilities are endless! Phong's Illumination Model Constant Diffuse Color Diffuse Texture Color Texture used as Label Texture used as Diffuse Color Lecture 15 Slide Fall 2002

26 Texture-Mapping Tricks Textures and Shading Combining Textures Bump Mapping Solid Textures Lecture 15 Slide Fall 2002

27 Shadow Maps Projectie Textures with Depth Textures can also be used to generate shadows. Will be discussed in a later lecture Lecture 15 Slide Fall 2002

Enironment Maps If, instead of using the ray from the surface point to the projected texture's center, we used the direction of the reflected ray to index a texture map.

28 Enironment Maps If, instead of using the ray from the surface point to the projected texture's center, we used the direction of the reflected ray to index a texture map. We can simulate reflections. This approach is not completely accurate. It assumes that all reflected rays begin from the same point. Lecture 15 Slide Fall 2002

29 What's the Best Chart? Lecture 15 Slide Fall 2002

30 Reflection Mapping Lecture 15 Slide Fall 2002

31 Questions? Image computed using the Dali ray tracer by Henrik Wann jensen Enironment map by Paul Debeec Lecture 15 Slide Fall 2002

32 Lecture 15 Slide Fall 2002

33 Texture Mapping Modes Label textures Projectie textures Enironment maps Shadow maps Lecture 15 Slide Fall 2002

34 The Best of All Worlds All these texture mapping modes are great! The problem is, no one of them does eerything well. Suppose we allowed seeral textures to be applied to each primitie during rasterization. Lecture 15 Slide Fall 2002

35 Multipass s. Multitexture Multipass (the old way) - Render the image in multiple passes, and "add" the results. Multitexture - Make multiple texture accesses within the rasterizing loop and "blend" results. Blending approaches: Texture modulation Alpha Attenuation Additie textures Weird modes Lecture 15 Slide Fall 2002

Texture Mapping in Quake Quake uses light maps in

Texture maps are used to add detail to surfaces,

36 Texture Mapping in Quake Quake uses light maps in addition to texture maps. Texture maps are used to add detail to surfaces, and light maps are used to store pre-computed illumination. The two are multiplied together at run-time, and cached for efficiency. Texture Maps Light Maps Data RGB Intensity Instanced Yes o Resolution High Low Light map image by ick Chirko Lecture 15 Slide Fall 2002

Bump Mapping Textures can be used to alter the surface normal of an object. This does not change the actual shape of the surface -- we are only shading it as if it were a different shape!

37 Bump Mapping Textures can be used to alter the surface normal of an object. This does not change the actual shape of the surface -- we are only shading it as if it were a different shape! This technique is called bump mapping. The texture map is treated as a single-alued height function. The alue of the function is not actually used, just its partial deriaties. The partial deriaties tell how to alter the true surface normal at each point on the surface to make the object appear as if it were deformed by the height function. Since the actual shape of the object does not change, the silhouette edge of the object will not change. Bump Mapping also assumes that the Illumination model is applied at eery pixel (as in Phong Shading or ray tracing). Swirly Bump Map Sphere w/diffuse Texture Sphere w/diffuse Texture & Bump Map Lecture 15 Slide Fall 2002

38 Bump mapping If Pu and P are orthogonal and is normalized: P = [ x( u, ), y( u, ), z( u, )] ormal = P u P P = P + B( u, ) T Initial point Simulated eleated point after bump P r P r' D D P u P + BuPu + BP D B u B Variation of normal in u direction = = B( s, t) B( s +, t) 2 B( s, t ) B( s, t + ) 2 Variation of normal in direction Compute bump map partials by numerical differentiation Lecture 15 Slide Fall 2002

39 Bump mapping General case P = [ x( u, ), y( u, ), z( u, )] = P u P ormal B( u, ) P = P + T Initial point Simulated eleated point after bump P u D P P u P + Bu u ( P ) B ( P ) D B u B Variation of normal in u direction = = B( s, t) B( s +, t) 2 B( s, t ) B( s, t + ) 2 Variation of normal in direction Compute bump map partials by numerical differentiation Lecture 15 Slide Fall 2002

40 Lecture 15 Slide Fall 2002 B B P P u u u u + + = B B P P + + = Bump mapping deriation u B P P ), ( + = P u P = 2 ) ( ) ( ) ( B B P B P B P P u u u u ery small... Assume B is 0 so and, But = = = P P P P u u u P B P B u u ) ( ) ( +

41 More Bump Map Examples Bump Map Cylinder w/diffuse Texture Map Cylinder w/texture Map & Bump Map Lecture 15 Slide Fall 2002

42 One More Bump Map Example otice that the shadow boundaries remain unchanged. Lecture 15 Slide Fall 2002

43 Displacement Mapping We use the texture map to actually moe the surface point. This is called displacement mapping. How is this fundamentally different than bump mapping? The geometry must be displaced before isibility is determined. Is this easily done in the graphics pipeline? In a ray-tracer? Lecture 15 Slide Fall 2002

44 Displacement Mapping Example It is possible to use displacement maps when ray tracing. Image from Geometry Caching for Ray-Tracing Displacement Maps by Matt Pharr and Pat Hanrahan. Lecture 15 Slide Fall 2002

45 Another Displacement Mapping Example Image from Ken Musgrae Lecture 15 Slide Fall 2002

Three Dimensional or Solid Textures The textures that we hae discussed to this point are two-dimensional functions mapped onto two-dimensional surfaces.

46 Three Dimensional or Solid Textures The textures that we hae discussed to this point are two-dimensional functions mapped onto two-dimensional surfaces. Another approach is to consider a texture as a function defined oer a three-dimensional surface. Textures of this type are called solid textures. Solid textures are ery effectie at representing some types of materials such as marble and wood. Generally, solid textures are defined procedural functionsrather than tabularized or sampled functions as used in 2-D (Any guesses why?) The approach that we will explore is based on An Image Synthesizer, by Ken Perlin, SIGGRAPH '85. The ase to the right is from this paper. Lecture 15 Slide Fall 2002

47 oise and Turbulence When we say we want to create an "interesting" texture, we usually don't care exactly what it looks like -- we're only concerned with the oerall appearance. We want to add random ariations to our texture, but in a controlled way. oise and turbulence are ery useful tools for doing just that. A noise function is a continuous function that aries throughout space at a uniform frequency. To create a simple noise function, consider a 3D lattice, with a random alue assigned to each triple of integer coordinates: Lecture 15 Slide Fall 2002

48 Turbulence oise is a good start, but it looks pretty ugly all by itself. We can use noise to make a more interesting function called turbulence. A simple turbulence function can be computed by summing many different frequencies of noise functions: One Frequency Two Frequencies Three Frequencies Four Frequencies ow we're getting somewhere. But een turbulence is rarely used all by itself. We can use turbulence to build een more fancy 3D textures... Lecture 15 Slide Fall 2002

49 Marble Example We can use turbulence to generate beautiful 3D marble textures, such as the marble ase created by Ken Perlin. The idea is simple. We fill space with black and white stripes, using a sine wae function. Then we use turbulence at each point to distort those planes. By arying the frequency of the sin function, you get a few thick eins, or many thin eins. Varying the amplitude of the turbulence function controls how distorted the eins will be. Marble = sin(f * (x + A*Turb(x,y,z))) Lecture 15 Slide Fall 2002

Texture-Mapping Tricks. How Bad Does it Look? We've Seen this Sort of Thing Before. Sampling Texture Maps

Texture-Mapping Tricks. How Bad Does it Look? We've Seen this Sort of Thing Before. Sampling Texture Maps Texture-Mapping Tricks Filtering Textures Textures and Shading Bump Mapping Solid Textures How Bad Does it Look? Let's take a look at what oversampling looks like: Click and drag the texture to rotate