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By J. Han

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View-frustum culling serves the purpose [9]. In a typical implementation of view-frustum culling, a large enough box or sphere bounding a polygon mesh is computed at the preprocessing step, and then at run time a CPU program tests if the bounding Vertex Processing 43 Fig. 15: If a polygon intersects the view frustum’s boundary, the part of the polygon outside the view frustum is discarded. volume is outside the view frustum. If it is, the polygon mesh is discarded and does not enter the rendering pipeline.

3 illustrates 2D rotation, where p is rotated about the origin by θ to define p . 4) represents the 2D rotation matrix. A 3D rotation requires the axis of rotation. First, consider rotation about the z -axis, which we denote by Rz . Suppose that it rotates (x, y, z) into (x , y , z ). 3) hold for the xy-coordinates. 6) represents Rz . , x, y, and z are replaced by y, z, and x, respectively. 8) −sinθ 0 cosθ Another frequently used transform in computer graphics is translation, which displaces (x, y, z) to (x + dx , y + dy , z + dz ).

Vn form a basis for the vector space V if and only if (1) v1 , v2 , . . , vn are linearly independent, and (2) v1 , v2 , . . , vn span V. Fig. 12 shows three examples of the basis for the 2D Euclidean vector space R2 . The standard basis is denoted by {e1 ,e2 }, where e1 = (1, 0) and e2 = (0, 1). There are many other bases that can be chosen for R2 . An example is {(2,1),(1,2)}. However, it is generally easier to work with an orthonormal basis, an orthogonal set of unit vectors, rather than an arbitrary basis.

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3D Graphics for Game Pgmg. (rev.) by J. Han


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