By Ronald Goldman

ISBN-10: 143980334X

ISBN-13: 9781439803349

Taking a singular, extra attractive method than present texts, An built-in creation to special effects and Geometric Modeling specializes in photographs, modeling, and mathematical equipment, together with ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector equipment, and transformation options. the writer starts off with fractals, instead of the common line-drawing algorithms present in many commonplace texts. He additionally brings the turtle again from obscurity to introduce a number of significant thoughts in special effects.

Supplying the mathematical foundations, the publication covers linear algebra themes, equivalent to vector geometry and algebra, affine and projective areas, affine maps, projective alterations, matrices, and quaternions. the most pics components explored contain mirrored image and refraction, recursive ray tracing, radiosity, illumination types, polygon shading, and hidden floor approaches. The ebook additionally discusses geometric modeling, together with planes, polygons, spheres, quadrics, algebraic and parametric curves and surfaces, optimistic reliable geometry, boundary documents, octrees, interpolation, approximation, Bezier and B-spline tools, fractal algorithms, and subdivision strategies.

Making the fabric available and proper for years yet to come, the textual content avoids descriptions of present photos and distinctive programming languages. as an alternative, it offers photographs algorithms according to well-established actual types of sunshine and cogent mathematical equipment.

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Extra resources for An Integrated Introduction to Computer Graphics and Geometric Modeling

Example text

Generate new fractal gaskets by changing the scaling parameter inside the body of the recursion for gaskets you have already generated. 6. 9. 7. 13. 13: A triangular pulse (left) and a rectangular pulse (right). 9. 8. 14. 14: Polygonal bumps: a pentagonal bump (left), a hexagonal bump (middle), and a polygonal bump with 20 sides (right). 9. 15. 15: More polygonal bumps. To generate these bumps, start at the left end point of the line at the base, proceed counterclockwise around the polygon, and finish at the right end point of the line.

11: The Law of Cosines provides a relationship between the length of a side and the distance from a vertex to the center of a regular polygon (left). Similarly, the Law of Cosines provides a relationship between the distance from a vertex to the center of a regular polygon and the length of each diagonal of the polygon. Notice that if the polygon has n sides, then b ¼ 2p=n. 7. Write a turtle program that for a regular polygon with an arbitrary number of sides draws: a. A wheel b. 8. 1, left. 9.

6: Levels 1, 3, 6 of a recursive turtle program for the Sierpinski gasket. Examining the syntax of the SIERPINSKI program, we see that the recursive body has a structure very similar to the program for generating a triangle. Applying this observation, we can easily generalize this program for the Sierpinski triangle to the following program that generates gaskets for arbitrary polygons. 7. 8. 7: Levels 1, 3, 5 of a recursive turtle program for a pentagonal gasket. 8: More fractal gaskets. 4). 2 19 Bump Fractals A bump curve is just a pulse along a straight line.

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