cg.pptx - HOMOGENEOU S COORDINATES Presented By Ahtesham Ullah Khan CS-3rd yr 1604610013 HOMOGENEOUS COORDINATES ◈ In mathematics homogeneous

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HOMOGENEOU S CO- ORDINATES Presented By: Ahtesham Ullah Khan CS-3 rd yr 1604610013

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HOMOGENEOUS COORDINATES In mathematics, homogeneous coordinates or projective coordinates , introduced by August Ferdinand Möbius in his 1827 . They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Homogeneous coordinates have a range of applications, including computer graphics and 3D computer vision , where they allow affine transformations and, in general, projective transformations to be easily represented by a matrix. If the homogeneous coordinates of a point are multiplied by a non-zero scalar then the resulting coordinates represent the same point.
Why we need Homogeneous Coordinates? One of the many purposes of using homogeneous coordinates is to capture the concept of infinity. If we don’t use homogeneous coordinates, it would be

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Unformatted text preview: difficult to design certain classes of very useful curves and surfaces. These curves and surfaces are very crucial in developing algorithms in computer vision, graphics, CAD, etc. ◈ We have seen that basic transformations can be expressed in matrix form. But many graphic application involve sequences of geometric transformations. Hence we need a general form of matrix to represent such transformations. OPERATIONS:-◈ Translation ◈ Shearing ◈ Rotation ◈ Reflection TRANSLATION X Y Z TRANSLATION ROTATION COORDINATE AXIS ROTATION X-AXIS ROTATION X-AXIS ROTATION Y Z X Y-AXIS ROTATION Y-AXIS ROTATION Y Z X Z-AXIS ROTATION Z-AXIS ROTATION Y Z X SCALING SCALING SCALING Y Z X REFLECTION REFLECTION REFLECTION SHEARING SHEARING SHEARING THAN K YOU...
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