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PPT5: Fundamental Geometric Algorithms
CAP 6736 Geometric Modeling PPT5: Fundamental Geometric Algorithms PPT and video are due no later than February 15 Submit to: This template file is just an outline of the presentation that you need to complete. Additional pages may be necessary to fully explore the topic above. Each page should contain adequate text as well as illustrations. You are free to use all publicly available information (text as well as graphics) as long as the sources are properly acknowledged.
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Team members’ contributions
Member [name]:
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Part I: Technical details
For this part you will need an equation editor. You may use: MS equation editor, MathType, LaTeX, or Handwritten equations if all else fails
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Knot Insertion Suggested content: Knot insertion Insert one knot
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Knot Insertion Suggested content: Knot insertion
Compute new control points and knots
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Knot Insertion Suggested content: Knot insertion example
New control points
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Knot Insertion Suggested content: Insert a knot multiple times
Triangular scheme of new control points
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Knot Insertion Algorithm
Suggested content: Knot insertion algorithm Pseudocode and examples
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Knot Insertion Suggested content: Applications of knot insertion
make entities compatible subdivide entities evaluating points and derivatives adding flexibility by adding more control points precise error control via symbolic operators symbolic algebra on curves and surfaces approximations via repeated knot refinement geometry processing
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Surface Knot Insertion
Suggested content: Surface knot insertion Insert a knot in one direction
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Surface Knot Insertion
Suggested content: Surface knot insertion Insert a knot in another direction
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Surface Knot Insertion
Suggested content: Surface knot insertion: split a surfaces Split in one direction
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Surface Knot Insertion
Suggested content: Surface knot insertion: split a surfaces Split in aanother direction
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Surface Knot Insertion
Suggested content: Surface knot insertion: split a surfaces Split in both directions
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Surface Knot Insertion
Suggested content: Surface knot insertion: iso-curves Extract iso-parametric curves
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Knot Refinement Suggested content: Curve knot refinement
Definition and example
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Knot Refinement Suggested content: Midpoint curve knot refinement
First and second refinement
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Surface Knot Refinement
Suggested content: Surface knot refinement In one and both directions
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Bezier Decomposition Suggested content:
Decompose NURBS curve into piecewise Bezier Use knot refinement
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Bezier Decomposition Suggested content:
Decompose NURBS surface into piecewise Bezier Use knot refinement
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Knot Removal Suggested content: Remove knots from NURBS curves
Basic definition
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Knot Removal Suggested content: Knot removal example
First, second and third derivative continuity General formula and algorithm sketch
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Knot Removal Suggested content: Curve knot removal examples
Single and multiple knot removals
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Knot Removal Suggested content: Surface knot removal examples
Single and multiple knot removals
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Degree Elevation Suggested content: Curve degree elevation
General formula NURBS-Bezier-degree elevate-NURBS paradigm Illustration of each step
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Degree Elevation Suggested content: Curve degree elevation examples
Elevate by one or more
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Degree Elevation Suggested content: Surface degree elevation examples
Elevate by one or more
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Degree Reduction Suggested content: Curve degree reduction
General formula NURBS-Bezier-degree reduce-NURBS paradigm Illustration of each step
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Bezier Degree Reduction
Suggested content: Bezier degree reduction General formula for even degree
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Bezier Degree Reduction
Suggested content: Bezier degree reduction General formula for odd degree
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Part II: Design examples
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Design Examples Suggested content:
Add design examples: images and or videos Give credit to the designers
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Part III: GM lab For this part of the assignment you may use an existing system, such as Blender, or write the code and visualize the result using graphics tools like Processing.
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Geometric Modeling Lab
Suggested project: Design B-spline curves using knot manipulation Use knot insertion for surface modeling
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