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3D Primitive and Composite Transformations
Previously you have studied and implemented 2D geometric transformations for object definitions in two dimensions. These transformations can be extended to 3D objects by including considerations for the z coordinate. In this unit, you will study certain methods to implement such transformations.
You must have noticed here that the translation is as simple as in 2D. Rotation however requires a little more effort in 3D. Standard rotations about three coordinate axes are simpler to perform. In order to apply rotation about an arbitrary axis, you need to have a composite transformation while scaling, shear and reflections are generalized to 3D in a natural way.
Polygon Surfaces - Curves and Surfaces By Figure 1 and Figure 2 it is clear that it is possible to store description of objects as a set of surface polygons and similar i
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To prove ‾P (1) = p n Solution : since in the above case we determine each term excluding B n,n (u) will have numerous of (1 - u) i (i = 0 to n) consequently by using u = 1
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De Casteljeau algorithm: The control points P 0 , P 1 , P 2 and P 3 are combined with line segments termed as 'control polygon', even if they are not actually a polygon although
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Linearly interpolate - Modeling and Rendering I 4 = I 1 + t (I 2 - I 1 ); here t = (|y 1 - y 2 |)/(|y 1 - y 2 |) I D = I A + t (I B - I A ); here t = (|AD|)/(|AB|)
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