Elementary Matrix Representation of Some Commonly Used Geometric Transformations in Computer Graphics and Its Applications
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چکیده
By using an extension of Desargues theorem, and the extended Desarguesian configuration thereof, the analytical definition for the stereohomology geometric transformation in projective geometry is proposed in this work. A series of such commonly used geometric transformations in computer graphics as central projection, parallel projection, centrosymmetry, reflection and translation transformation, which can be included in stereohomology, are thus analytically defined from this point of view. It has been proved that, the transformation matrices of stereohomology are actually equivalent to the existing concept in numerical analysis: elementary matrices. Based on the meaning of elementary matrices in projective geometry thus obtained, a novel approach of 3D reconstructing objects from multiple views is proposed together with some of the concepts, principles and rules for its applications in computer graphics.
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