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Unformatted text preview: CS 551/651 Advanced Computer Graphics Warping and Morphing Spring 2002 Deforming Objects Changing an objects shape Usually refers to nonsimulated algorithms Usually relies on user guidance Easiest when shape number of faces and vertices is preserved Define the movements of vertices Moving Vertices Time consuming to define the trajectory through space of all vertices Instead, control a few seed vertices which in turn affect nearby vertices Defining Vertex Functions If vertex i is displaced by (x, y, z) units Displace each neighbor, j , of i by (x, y, z) * f (i, j) f (i,j) is typically a function of distance Euclidean distance Number of edges from i to j Distance along surface Vertex Displacement Function i is the (shortest) number of edges between i and j n is the max number of edges affected ( k =0) = linear; ( k <0) = rigid; ( k >0) = elastic Figure 3.55 ; 1 . 1 ) ( ; 1 . 1 ) ( 1 1 < + = + = + + k n i i f k n i i f k k 2D Grid Deformation 1974 film Hunger Draw object on grid Deform grid points Use bilinear interpolation to recompute vertex positions on deformed grid Draw example on board Figure 3.57 Polyline Deformation Draw a piecewise linear line (polyline) through the geometry For each vertex compute...
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 Fall '10
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 Algorithms, Computer Graphics

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