COMP410 Texture Mapping

where does texture mapping take place?

fragment processor

what is the idea?

mapping from some dimension to another dimension

the coordinate systems that might be involved in texture mapping

parametric coordinates (u,v), texture coordinates (s,t), object/world coordinates (x,y,z), screen coordinates

what are parametric coordinates used for?

to model curved surfaces

what is the direction we want to find in texture mapping

given a point on the object we’d rater like to know which point in the texture it corresponds to

so in a sense:

s = s(x,y,z)

t = t(x,y,z,)

0 <= s, t <= 1

how does texture mapping kinda work?

for object vertices on the world map you will have (via algorithm or explicitly given) coordinates on the texture, and then you could map it via bilinear interpolation.

issue with bilinear interpolation

may cause distortions when texutre is mapped on a trianglea

aliasing

point sampling of the texture can lead to aliasing errors

a better option for anti aliasing

using are averaging

magnification

one texel may cover many pixels

minification

many texels may cover a single pixel

mipmapping

allows for prefiltered texture maps of decreasing resolutions

one option for genertaing texture coordinates if they are not explicitly given?

specify a plane near the object, and then generate texture coordinates based upond distance from that plane.

two point mapping approach

map to some intermediate object, and then map to actual object.

cylinder as the intermediate object, two point mapping

x = r*cos(2pi*u)

y = r*sin(2pi*u)
z = v.h

notice that this is a parametric form, hence u = s, and v = t.

parametric sphere, two point mapping

x=rcos(pi*u)

y = rcos(pi*u)*cos(2pi*v)

z = r*sin(pi*u)*sin(2pi*v)

one thing to consider with sphere mapping, two point

need to decide where to put the distortion (at the poles e.g.)

spherical maps are expecially used in

environmental mapping

box mapping

like minecraft skins

second part of two point mapping

what if the object is not a sphere cylinder, or a box,

then on the object

use normals from the intermediate to actual

use normals from actual to intermediate

use vectors from the center of the intermediate

what does culling enable

we can avoid rendering triangles facing away from the viewer by culling.

culling predicate

a face is visible if -90 <= the angle between the normal and the viewer vector <= 90

or equivalently, if 0 <= v.n