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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 Rendering and Ray Tracing Methods In previous section we had discussed various methods for visible-surface detection, although in order to produce visibility the prese
Area subdivision Method - Visible Surface Detection What are the circumstances to be fulfilled, in Area-subdivision method, thus a surface not to be divided in addition? S
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Mathematics: There are some area like Probability, combination, permutation, etc.,that can be well explained along with the help of animation, that helps in enhancing the learning
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Illumination Model - Polygon rendering and ray tracing methods Theoretically illumination is exposure of a thing to the light that contributes to light reflected by an object
Bezier curves: Theses are special polynomial curves expressed using Bernstein polynomials. Spline curves are simple extensions of Bézier curves composed of two or more polynom
Proof of subsequent properties of Bezier curves Note: Proof of subsequent properties of Bezier curves is left as a work out for the students P' (0) = n (p 1 - p 0 ) P
2-D and 3-D Transformations Previously, we have presented approaches for the generation of polygonal regions and lines. We identified that once the objects are produced, the v
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