Geometric Modeling with Splines (CS6670)
This course is an introduction to the current concepts and issues in CAGD systems with emphasis on free-form surface design. It also includes mathematics of free-form curve and surface representations, including Coons patches, Bezier methods, B-splines, triangular interpolants, and their geometric consequences. Classical surface geometry, local and global design tradeoffs, explicit and parametric tradeoffs, and subdivision and refinement as techniques in modeling were also included.
Exercise No1:
The goal of this exercise was to make us familiarize with setting up implicit equations for pencils of conics from the line equation.
Exercise No2:
The goal of this exercise was to make us familiarize with setting up the implicit equations for pencils of conics in the “3-point” form from the line equations.
Exercise No3:
The goal of this exercise was to make us familiarize with derivation and evaluation of Bezier curves and its derivatives. I also dealt with compound curves and its properties.
Exercise No4:
The goal of this exercise was to make us familiar with computation of frenet frame, curvature, torsion and derivative forms of a Bezier curve.
Exercise No5:
The goal of this exercise was to make us familiar with concepts of B-splines and interpolation methods like complete cubic spline interpolation and cubic nodal interpolation.
Programming Exercise No1:
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The main aim of the assignment was to produce a graphics program, which helps the user to create and edit 2D Bezier curves. The user should also be given options like opening any curve dataset file and editing them. The second part of the program was to allow the user to create and edit 2D Rational Bezier curves.
Programming Exercise No2:
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The main aim of the assignment was to produce a graphics program, which helps the user to view 3D polynomial B-spline surfaces using isolines. The user should be allowed to open any 3D polynomial Bspline surface dataset file and display isoparametric curves at nodal values and Knot values in each direction. The second part of the assignment was to create surface that interpolates to a grid of data with nodal interpolation. The user should be allowed to read grid
data from file and allowed to select degrees of interpolation in each direction. Using the selected degrees of the interpolation, appropriate knot vectors should be created and using in the interpolation of surface.
Programming Exercise No3:
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The main aim of the assignment was to produce a graphics program, which helps the user to view 3D polynomial B-spline surfaces using isolines. The user should be allowed to open any 3D polynomial Bspline surface dataset file and display isoparametric curves at nodal values and Knot values in each direction. The second part of the assignment was to create surface that interpolates to a grid of data with nodal interpolation. The user should be allowed to read grid
data from file and allowed to select degrees of interpolation in each direction. Using the selected degrees of the interpolation, appropriate knot vectors should be created and should be used in the interpolation of surface.