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Basic Transformations - 2-d and 3-d Transformations
Consider the xy-coordinate system upon a plane. An object or Obj in a plane can be identified as a set of points. All object point P has coordinates (x,y), consequently the object is the total sum of every its coordinate points as in figure. Here the object is moved to a new position. Every coordinate points P'(x',y') of a new object Obj' can be acquired from the original points P(x,y) through the application of a geometric transformation.
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Important points about the bezier curves - modeling and rendering 1) Generalizing the idea of Bezier curve of degree at n based upon n+1 control point p0,.....pn P(0)= P 0
To prove: P (u = 0) = p0 Solution : = p 0 B n,0 (u) + p 1 B n, 1 (u) +...... + p n B n, n (u)...............(1) B n,i (u) = n c i u i (1 - u) n-i B n,0
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