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Material Type: Notes; Professor: Jacobs; Class: Computer Graphics; Subject: Computer Science; University: University of Maryland; Term: Fall 2009;
Typology: Study notes
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Interpolate between corners to get two points on sides collinear with middle point. Then interpolate between these.
Or, represent p as weighted average of p1, p2, p3, and take same weighted average of f(p1), f(p2), f(p3). Ie, find a, b, c so that
p = ap1 + bp2 + c*p3, a+b+c=1 and find
f(p) = af(p1) + bf(p2) + c*f(p3).
These produce the same result.
Bilinear Interpolation – 4 points
If we interpolate to get f(x,0) = (1-x)f(0,0)+xf(1,0), f(x,1) = (1-x)f(0,1) + xf(1,1). Then f(x,y) = ((1-x)f(0,0)+xf(1,0))(1-y) + (f(x,1) = (1-x)f(0,1) + xf(1,1))y. If we interpolate to get f(0,y) = (1-y)f(0,0) + yf(0,1), f(1,y) = (1-y)f(1,0) + y(f(1,1). Then f(x,y) = ((1-y)f(0,0) + yf(0,1))(1-x) + ((1-y)f(1,0)+y(f(1,1)))x These are the same.
Instead of weighting by distance, d, weight by:
1 – 3d^2 + 2|d|^3
•Smooth
•Symmetric
