Achieve a perspective projection on the plane of unit cube, Computer Graphics

Achieve a perspective projection on the z = 0 plane of the unit cube, demonstrated in Figure (l) from the cop at E (0, 0, 10) upon the z-axis.

564_Achieve a Perspective Projection on the Plane of Unit Cube.png

Figure: I

01:  currently center of projection

E = (0, 0, -d) = (0, 0, 10).

∴ d = - 10

We identify here (from equation - 1), the particular point perspective transformation of the projection along with z = 0, plane; here cop is at (0, 0, -d) is provided by:

134_Achieve a Perspective Projection on the Plane of Unit Cube 1.png

--------------------------(I)

Pn' = P. Pper, z                                                                     --------------- (II)

Hence the perspective transformation of a provided cubes v = [ABCDEFGH] to V' = [A'B'C'D'E'F'G'H'] with d = - 10 is provided by:

[V'] = [V] . [Pper, z]

1957_Achieve a Perspective Projection on the Plane of Unit Cube 2.png

Hence the projected points of a provided cube V = [ABCDEFGH] are as:

A' =(0, 0, 0), B' = (1.11, 0, 0), C' = (1.11, 1.11, 0), D' = (0, 1.11, 0), E' = (0, 0, 0) F' = (1, 0, 0), G' = (1, 1, 0) and H' = (0, 1, 0).

Posted Date: 4/4/2013 3:19:38 AM | Location : United States







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