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Vanishing Point - Viewing Transformations
This point is that point at those parallel lines shows to converge and vanish. A practical illustration is a long straight railroad track.
To demonstrate this idea, consider the Figure 17 that appears a perspective transformation onto z=0 plane. The Figure17 appears a Projected line A*B* of specified line AB parallel to the z-axis. The center of projection is at (0,0,-d) and z=0 be the projection plane.
Identify the perspective transformation of the point at infinity on the +z-axis, that is:
Hence, the ordinary coordinates of a point (x',y',z',1)=(0,0,0,1), consequent to the transformed point at infinity upon the z-axis, is here a finite point. This implies that the whole semi-infinite positive space (0<=z<=∞) is transformed to the finite +ive half space 0<=z'<=d.
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Proof of subsequent properties of Bezier curves Note: Proof of subsequent properties of Bezier curves is left as a work out for the students P' (0) = n (p 1 - p 0 ) P
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De Casteljeau algorithm: The control points P 0 , P 1 , P 2 and P 3 are combined with line segments termed as 'control polygon', even if they are not actually a polygon although
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Important Points About the Diffuse Reflection An extremely rough surface appears uniformly bright from each viewing direction Q the intensity of reflected light is identical i
Phong shading OR Normal Vector Interpolation Shading In Gouraud shading we were doing direct interpolation of intensities although a more exact method for rendering a polygon
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