David S. Ebert
September 2000
Map in object space
In texture space for quadrilaterals
P_{1v} = P_{10} + v (P_{11} - P_{10})
P_{uv} = P_{0v} + u (P_{1v} - P_{0v})
P_{uv} = {P_{00} + v (P_{01} - P_{00})} + u{ (P_{10} + v (P_{11} - P_{01})) - (P_{00} + v (P_{10} - P_{00}))}
...solve for u and v.
In general case, add P_{ij}'s u,v coordinates into equation.
Before do this,
Now what do you do ?
Solution: Antialiased texture mapping
Use square root of texture area subtended by pixel
Other Mapping Functions
How do we calculate F_{u}, F_{v}?
How do we calculate P_{u}, P_{v}?
Dependence on scale:
If scale object, need to adjust displacement map accordingly