Download 3D Computer Graphics : A Mathematical Introduction with by Samuel R. Buss PDF

By Samuel R. Buss

This creation to 3D special effects emphasizes basics and the math underlying special effects, whereas additionally overlaying programming options utilizing OpenGL, a platform-independent portraits programming atmosphere. The minimum necessities make it compatible for self-study or to be used as a complicated undergraduate or introductory graduate textual content because the writer leads step by step from the fundamentals of modifications to complicated issues reminiscent of animations and kinematics. Accompanying software program, together with resource code for a ray tracing software program package deal, is obtainable freely from the book's site.

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Additional info for 3D Computer Graphics : A Mathematical Introduction with OpenGL

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The stages of the pipeline are as follows: Modeling. In this stage, a 3-D model of the scene to be displayed is created. This stage is generally the main portion of an OpenGL program. The program draws images by specifying their positions in 3-space. At its most fundamental level, the modeling in 3-space consists of describing vertices, lines, and polygons (usually triangles and quadrilaterals) by giving the x-, y-, z-coordinates of the vertices. OpenGL provides a flexible set of tools for positioning vertices, including methods for rotating, scaling, and reshaping objects.

4 Every rigid, orientation-preserving, affine transformation is either a translation or a generalized rotation. Obviously, the converse of this theorem holds too. Proof Let A be a rigid, orientation-preserving, affine transformation. Let u = A(0). 2 implies that A is a rotation. So suppose u = 0. It will suffice to prove that either A is a translation or there is some point v ∈ R2 that is a fixed point of A, that is, such that A(v) = v. 2 shows that A is a generalized rotation around v. Let L be the line that contains the two points 0 and u.

10(a) if M is the identity matrix. 10. Drawing points (a) without transformation by the model view matrix and (b) with transformation by the model view matrix. The matrix is as given in the text and represents a rotation of −90◦ degrees followed by a translation of 1, 3 . 10(b). Fortunately for OpenGL programmers, we do not often have to work directly with the component values of matrices; instead, OpenGL lets the programmer specify the model view matrix with a set of calls that implement rotations and translations.

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