Applied Graphics and Geometry
Interactive Examples (AGGIE-Volume 2)
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Department of Mechanical Engineering

Each lecture below contains a Task, Theory, Solutions and Review Questions that
complement classroom lectures and self paced study. Mathcad 2001i Professional-Academic edition is used.

Users external to USNA will need Mathcad 2001i or higher to read the .mcd files.

Scroll screen down to view the entire Index and click on lecture of choice.

Preface(preface.htm)

Chapter 1:  Introduction to Parametric Surfaces

•  Design using Analytical Surfaces(I-1.htm)
•  Parametric Lofted Surface(I-2.htm)
•  Modified Torus Surface(I-3.htm)
• Parabolically Blended Surfaces of Revolution(I-5.htm)
• Surface Assembly(I-6.htm)
• Further Surface Assembly(I-7.htm)
• Vertical Helix Surface(I-8.htm)
• Line Sweep with Rotation(I-9.htm)
• Cubic Spline Sweep Surface(I-10.htm)
• Piecewise Cubic Spline Sweep Surface(I-11.htm)
• Complex Sweep Surfaces(I-12.htm)
• Bilinear Surface(I-13.htm)
• Lofted Surface(I-14.htm)
• Surface Area of Parabolically Blended Surface(I-15.htm)
• Analytical and Lofted Surface Patches(I-16.htm)
• Practical Analytical Shapes(I-17.htm)
• Cycloid Surface of Revolution(I-18.htm)
• Intersection between Ellipse and Hyperbola(I-19.htm)
• Normal Distribution Function(I-20.htm)
• Chapter 2:  Bezier and B-Spline Surfaces
• Bezier Surface of Revolution(II-1.htm)
• Bi-cubic Bezier Surface Patch(II-2.htm)
• Bezier Surface Patch using 5x3 Surface Net(II-3.htm)
• Sail Shape using 4x4 Bezier Surface(II-4.htm)
• Sail Shape using a 4x6 Bezier Surface(II-5.htm)
• Sail Shape Surface Area(II-6)
• Cartesian Product B-Spline Surface(II-7.htm)
• 3rd Order B-Spline Surface(II-8.htm)
• Surface of Mixed Order(II-9.htm)
• Periodic B-Spline Surface(II-10.htm)
• Toroidal Surface using B-Spline(II-11.htm)
• B-Spline Sweep Surface(II-12.htm)
• B-Spline Surface of Revolution(II-13.htm)
• Bezier and B-Spline Surfaces of Revolution using Three Vertices(II-14.htm)
• Bezier and B-Spline Surfaces of Revolution using Six Vertices(II-15.htm)
• Converging-Diverging Nozzle(II-16.htm)

Chapter 3:  Rational B-Spline Surfaces

• Ruled Rational B-Spline Surface between 3rd Order Boundaries(III-1.htm)
• Ruled Rational B-Spline Surface between 4th Order Boundaries(III-2.htm)
• Comparison of Regular and Rational B-Splines(III-3.htm)
• B-Spline Surface with Duplicate Vertices in Polygon Matrix(III-4.htm)
• Effect of Local Homogeneous Coordinates(III-5.htm)
• Modified Rational B-Spline Surface Design(III-6.htm)
• Toroidal Surface(III-7.htm)
• Rational B-Spline Surfaces of Revolution(III-8.htm)
• Rational B-Spline Surface of Revolution with Double Polygon Vertex(III-9.htm)
• Symmetrical Surface with Non-circular Cross Sections(III-10.htm)
• Trim Surface Design using Open B-Spline Basis in both Directions(III-11.htm)
• Trim Surface Design with Open and Periodic Basis(III-12.htm)
• B-Spline Surface Patch between Elliptical and Circular Boundaries(III-13.htm)
• Sweep Surface Modification(III-14.htm)
• Pseudo Spherical and Spherical Surfaces(III-15.htm)
• Non-Spherical Surfaces(III-16.htm)
• Ducts with various Cross Sections(III-17.htm)
• Mixed B-Spline Ruled Surface(III-18.htm)
• Duct with variable Cross Sectionsl Areas(III-19.htm)
• B-Spline Surface Pressure Vessel(III-20.htm)

Chapter 4: Design with Non-Uniform Rational B-Splines(NURBS)

• Linear Coons Surface between B-Spline Boundaries(V-1.htm)
• B-Spline Boundaries with Repeated Internal Vertices(V-2.htm)
• Linear Coons Surface(V-3.htm)
• Coons Bicubic Surface Patch(V-4.htm)
• Bezier Surface using Blending Matrix for 5x3 Surface Net(V-5.htm)
• Bezier Surface using Blending Matrix for 4x4 Surface Net(V-6.htm)
• Linear Coons Surface between Bezier Boundaries(V-7.htm)
• Bezier Surface with First and Second Derivatives(V-8.htm)
• Gaussian and Average Curvature for Bezier Surface(V-9.htm)
• Bezier Surface and First Derivatives(V-10.htm)
• Regular B-Spline Surface(V-11.htm)
• Closed Periodic B-Spline Surface(V-12.htm)
• Toriodal Surface with Twist(V-13.htm)
• Curvatures for a Mixed Order B-Spline Surface(V-14.htm)
• 3rd Order Rational B-Spline Surface using 4x4 Net(V-15.htm)
• Effect of Zero Values in the Homogeneous Vector(V-16.htm)
• Toroidal Surface of Conic Cross-Section with Periodic Basis(V-17.htm)
• Matching B-Spline Surface to Analytical Surface(V-18.htm)
Chapter 6:  Review Examples
• Conical Surface of Revolution(VI-1.htm)
• Torus Surfaces(VI-3.htm)
• Bezier Surface of Revolution(VI-4.htm)
• Helical Surfaces(VI-5.htm)
• Cubic Spline Sweep Surface(VI-6.htm)
• Sweep Surface with Axis Rotation(VI-7.htm)
• Sweep Surface with Circular Cross Section(VI-8.htm)
• Surface Patch Derivatives on a Unit Sphere(VI-9.htm)
• Parametric Surface Mappping(VI-10.htm)
• Ruled Surface between Conic Sections(VI-11.htm)
• Ruled Surface between a B-Spline Conic and Ellipse(VI-12.htm)
• Gaussian and Average Curvature(VI-13.htm)
• Rational B-Spline Ruled Surface using 3x3 Net(VI-14.htm)
• B-Sokube Ruled Surface(VI-15.htm)
• Rational B-Spline Surface of Revolution(VI-16.htm)
• 3rd Order Rational B-Spline Surface Patch(VI-17.htm)
• Hemispherical Surface of Unit Radius(VI-18.htm)
• Regular and Rational B-Spline Surfaces of Cylindrical Topology(VI-19.htm)
• Bilinear Surface using Parametric Functions(VI-20.htm)