Mathematics : Computational Geometry
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1. Two dimensional Transformations |
1. Two dimensional Transformations
1. Introduction, Representation of Points, Transformations and Matrices, Transformation of Points
2. Transformation of Straight Lines, Midpoint Transformation, Transformation of Parallel Lines,
Transformation of Intersecting Lines, Rotation, Reflection, Scaling, Combined Transformations,
3. Transformation of the Unit Square, Solid Body Transformation, Translations and Homogeneous
Coordinates, Rotation About an Arbitrary Point, Reflection Through an Arbitrary Line
4. Projection - A Geometric Interpretation of Homogeneous Coordinates, Overall Scaling, Points at
Infinity.
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2. Three Dimensional Transformations |
2. Three Dimensional Transformations 1. Three Dimensional Scaling and Shearing, Three Dimensional Rotation. Three Dimensional
Reflection. Three Dimensional Translation. Multiple Transformations
2. Rotations about an Axis
Parallel to a coordinate axis, Rotation about an Arbitrary Axis in Space, Reflection Through an
Arbitrary Plane
3. Affine and Perspective Geometry, Orthographic Projections, Axonometric Projections, Oblique Projections, Perspective Transformations. Techniques for generating
perspective views, Vanishing points
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3. Plane Curves |
3. Plane Curves
1. Curve representation, non-parametric curves, parametric curves, parametric representation of a
circle
2. parametric representation of an Ellipse, parametric representation of a parabola,
parametric representation of a Hyperbola
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4. Space Curves Beizer curves |
4. Space Curves Beizer curves
1. Introduction, definition, properties (without proofs)
2. curve fitting (up to n = 3), equation of the curve in matrix form (up to n = 3)
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