Games with Texture Mapping Steve Marschner CS 4620 Cornell University Cornell CS4620 Fall 2020 Steve Marschner • 1
Recall first definition… Texture mapping: a technique of defining surface properties (especially shading parameters) in such a way that they vary as a function of position on the surface. Cornell CS4620 Fall 2020 Steve Marschner • 2
A refined definition Texture mapping: a set of techniques for defining functions on surfaces, for a variety of uses. Let’s look at some examples of more general uses of texture maps. Cornell CS4620 Fall 2020 Steve Marschner • 3
Reflection mapping • Early (earliest?) non-decal use of textures • Appearance of shiny objects – Phong highlights produce blurry highlights for glossy surfaces. – A polished (shiny) object reflects a sharp image of its environment. • The whole key to a shiny-looking material is [Dror, Willsky, & Adelson 2004] providing something for it to reflect. (a) (b) Figure 2. (a). A shiny sphere rendered under photographically acquired real-world illumination. (b). The same sphere rendered under illumination by a point light source. Cornell CS4620 Fall 2020 Steve Marschner • 4
Hand with Re fm ecting Sphere . M. C. Escher, 1935. lithograph
Reflections in ray tracing • Recall how we can make mirror reflections in ray tracing n r v r = v + 2(( n · v ) n − v ) = 2( n · v ) n − v Cornell CS4620 Fall 2020 Steve Marschner • 6
Reflection mapping • If scene is infinitely far away, the color seen by the reflection ray depends only on the direction of the ray – a two-dimensional function – represent it with a texture! • Environment map: texture that maps directions to colors – one option: axes are (theta, phi) – better option: cube map Cornell CS4620 Fall 2020 Steve Marschner • 7
straight up straight up straight up due East due South due West due North due East straight down straight down straight down A spherical panorama, aka. enironment map openfootage.net
Environment map • A function from the sphere to colors, stored as a texture. [Blinn & Newell 1976] Cornell CS4620 Fall 2020 Steve Marschner • 9
Spherical environment map � r � 1 r � Hand with Re fm ecting Sphere . M. C. Escher, 1935. lithograph Cornell CS4620 Fall 2020 Steve Marschner • 10
Environment Maps [Paul Debevec] Cornell CS4620 Fall 2020 Steve Marschner • 11
Cube map ( u , v ) = (1, 1) x = y = z right face has x > | y | and x > | z | ( u , v ) = (0, 0) x = – y = – z a direction vector maps to the point on the cube that is along that direction. The cube is textured with 6 square texture maps. Cornell CS4620 Fall 2020 Steve Marschner • 12
[Zephyris at en.wikipedia] [Emil Persson] Cornell CS4620 Fall 2020 Steve Marschner • 13
Reflection mapping in GLSL • A fragment operation – requires surface normal and a way to get the view direction • GLSL handles cubemaps by itself – you just give it the reflection vector and it figures out where to sample and on which face – sample using textureCube() • Don’t overlook built-in functions – e.g. reflect() Cornell CS4620 Fall 2020 Steve Marschner • 14
Displacement mapping • A powerful tool for modeling detail – used heavily in film production • Geometric prerequisites – texture map representing height field – smooth normals – texture coordinates – dense triangulation • In GLSL – a vertex operation (because it moves geometry) – displace vertices along normals according to texture map value – compute new normal to displaced surface (depends on the slope of the displacement texture) Cornell CS4620 Fall 2020 Steve Marschner • 15
[wikiwand]
base surface hand-painted displacement map (detail) Pawe ł Filip displaced surface tolas.wordpress.com Cornell CS4620 Fall 2020 Steve Marschner • 17
Displacement mapping • A powerful tool for modeling detail – used heavily in film production • Geometric prerequisites – texture map representing height field – smooth normals – texture coordinates – dense triangulation • In GLSL – a vertex operation (because it moves geometry) – displace vertices along normals according to texture map value – compute new normal to displaced surface (depends on the slope of the displacement texture) Cornell CS4620 Fall 2020 Steve Marschner • 19
Bump mapping • Displacement mapping is expensive – requires densely tessellated geometry – many triangles to rasterize • For small displacements, change in normal is most important – so just do that part; don’t displace the surface • Bump mapping is then a fragment operation – doesn’t require dense tessellation – doesn’t actually displace the surface – gives shading that looks just like displaced surface Cornell CS4620 Fall 2020 Steve Marschner • 20
INI, sznple results that can be achieved with this IDI, technique. The first pattern, a hand drawn unit tan+ sqrt(Fu'+Fv') cell of bricks was mapped onto the sphere on the cover. sqrt(Fu'+Fv.') lNl/lDl INI/IDI ID’1 INI 50 tan+' ID'l/lNl Bump mapping - -. Figure 8 Hand Drawn Functions [Blinn 1978] : Cornell CS4620 Fall 2020 Steve Marschner • 21
[CS467 slides] Geometry Bump Displacement mapping mapping
[CS467 slides] Geometry Bump Displacement mapping mapping
Bump mapping • Displacement mapping is expensive – requires densely tessellated geometry – many triangles to rasterize • For small displacements, change in normal is most important – so just do that part; don’t displace the surface • Bump mapping is then a fragment operation – doesn’t require dense tessellation – doesn’t actually displace the surface – gives shading that looks just like displaced surface Cornell CS4620 Fall 2020 Steve Marschner • 24
Normal mapping • Bump mapping is great – great way to add detail with low cost – bump textures are great for authoring detail • But it requires computing slope of displacement – have to take multiple samples from texture – precision issues easily lead to artifacts • So just compute the normal ahead of time – takes a bit more memory, but so be it – usually stored in a tangent space coordinate system defined by the normal vector and two tangent vectors • Normal mapping is so common it’s sometimes just called “bump mapping” Cornell CS4620 Fall 2020 Steve Marschner • 25
A normal map Cornell CS4620 Fall 2020 Steve Marschner • 26
A normal map Cornell CS4620 Fall 2020 Steve Marschner • 27
A normal map RGB color = XYZ normal Cornell CS4620 Fall 2020 Steve Marschner • 27
A normal map RGB color = XYZ normal R = X component (u direction) Cornell CS4620 Fall 2020 Steve Marschner • 27
A normal map RGB color = XYZ normal R = X component (u direction) G = Y component (v direction) Cornell CS4620 Fall 2020 Steve Marschner • 27
A normal map RGB color = XYZ normal R = X component (u direction) G = Y component (v direction) B = Z component (n direction) Cornell CS4620 Fall 2020 Steve Marschner • 27
Cornell CS4620 Fall 2020 Steve Marschner • 28
Cornell CS4620 Fall 2020 Steve Marschner • 28
Normal mapping [Paolo Cignoni] Cornell CS4620 Fall 2020 Steve Marschner • 29
Normal mapping • Geometric prerequisites – mesh with smooth normals and texture coordinates – no dense triangulation needed – unit tangent vectors (normalized, orthogonal) – texture map (3 channels) representing normal field • Fragment shader logic – look up normal from map in (tangent-u, tangent-v, normal) space – no finite differencing needed – transform normal into eye (or world) space – use interpolated normal and tangents for this – compute shading as always Cornell CS4620 Fall 2020 Steve Marschner • 30
Computing tangent vectors • How do we get these tangent vectors? – they need to be stored at vertices on the mesh, like normals • For a triangle, there’s a unique linear map from (u,v) to (x,y,z) – the derivatives of that map are the (non-unit) tangents – can be computed by solving three 2x2 linear systems – math resembles triangle setup for rasterization; details here • For displacement/bump mapping you want to leave the tangents unnormalized and non-orthogonal • For normal mapping and other uses it’s often handy to make the two tangents and the normal into an ONB – use exactly the basis-from-two math that we have used for cameras and manipulators Cornell CS4620 Fall 2020 Steve Marschner • 31
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