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CG-lecture02-3 - Computer Graphics Lecture 2-3 Geometric...

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Computer Graphics Lecture 2-3 Geometric Transformation used in OpenGL
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Remember? (1) We only consider one point in complex geometric graphics. And we refer it as observed vector . (2) The row or column vectors in a matrix are basis vectors .
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How to describe graphics with vectors ? glBegin(GL_XXX); …… glEnd();
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Transformation in 3D pipeline 1. Local-World system transformation 2. World-Viewing system transformation 3. Perspective Projection transformation
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1. Local-World system transformation (1) Vector transformation (2) Coordinate System transformation
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A 2D example Scale Rotate Translate Scale Translate X Y World Coordinates Local Coordinates Y W X W
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(1) Vector transformation X Y Local Coordinates Initial location at (0, 0) with x- and y-axes aligned Y W X W Y X
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(1) Vector transformation Scale 0.3, 0.3 Rotate -90 Translate 1, 9 Y X X Y Local Coordinates
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(1) Vector transformation X Y Local Coordinates Y X Scale 0.3, 0.3 Rotate -90 Translate 1, 9
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(1) Vector transformation X Y Local Coordinates Y X Scale 0.3, 0.3 Rotate -90 Translate 1, 9
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= 1 1 0 0 0 1 0 0 0 1 1 Y X Y X V V V V (1) Vector transformation Identity Vector Transformation (Local system is equal to World system) Vector Transformation in the example Scaling Rotation Translation
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