Interactive Examples (AGGIE-Volume 1)

URL()

J. Alan Adams, Ph.D.

Department of Mechanical Engineering

United States Naval Academy

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.

Use **Microsoft Internet Explorer**
to download the .mcd files to your computer.

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

Preface(preface.htm)

Chapter 1: Graphic Transformations

Chapter 2: Geometric ModelingRotation of Data to Create Orthographic Views at Specified Eye Position(I-1.htm) Rotation of Data to Create Orthographic Views from Normal Eye Position(I-2.htm) Isometric Projection(I-3.htm) Use of Homogeneous Coordinates to Create Orthographic Views(I-4.htm) Translation and Rotatiion using Homogeneous Coordinates(I-5.htm) Rotations and Projections(I-6.htm) Noncommutative Nature of 3D Rotations(I-7.htm) Rotation and Translation(I-8.htm) Projections of a Trapezoid(I-9.htm) Interpretatiion of Surface Plots(I-10.htm) Trimetric Projection(I-11.htm) Isometric and Dimetric Projections(I-12.htm) Simple Origami of Triangular Facets(I-13.htm) Rotation about a Local Axis(I-14.htm) Reflection through a Plane(I-15.htm) Right Hand and Left Hand Coordinates(I-16.htm) Local Scaling and Transformation(I-17.htm) Overall Scaling(I-18.htm) Local Shearing(I-19.htm) Order of 3-D Rotations(I-20.htm) Rotation about Parallel Principal Axes(I-21.htm) Multiple Rotations about Parallel Principal Axes(I-22.htm) Perspective Transformations(I-23.htm) One and Two Point Perspectives of I-Beam(I-24.htm) Perspective Views and Vanishing Points of a Prism(I-25.htm) Stereo Pair(I-26) Arbitrary Plane of Projection(I-27.htm) Three Dimensional Reconstruction(I-28) Transformation Reconstruction(I-29) Transformation Reconstruction using Two Photographs(I-30)

- Normal to a Plane(II-1.htm)
- Edge View of a Plane(II-2.htm)
- Planes in True Size(II-3.htm)
- Assembly of Line and Planes(II-4.htm)
- Line seen as a Point(II-5.htm)
- Line seen in True Length(II-6)
- Parallel Lines(II-7.htm)
- Implicit Plane parallel to a Plane(II-8.htm)
- Plane containing Points and parallel to a Line(II-9.htm)
- Shortest Distance form Point to Line(II-10.htm)
- Shortest Distance from Point to Plane(II-11.htm)
- Plane perpendicular to Line(II-12.htm)
- Shortest Distance from Origin to Plane(II-13.htm)
- Intersection between Line and Plane(II-14.htm)
- Parametric Equations for a Plane and Line(II-15.htm)
- Projection of Line onto a Plane(II-16.htm)
- Shortest Distance between Skew Lines(II-17.htm)
- Shortest Distance between Two Lines with Given Slope(II-18.htm)
- Vertical Distance between Two Skew Lines(II-19.htm)

Chapter 3: Geometric Construction

- Circle in 3D Space with given Diameter(III-1.htm)
- Circle in 3D Space through Three given Points(III-2.htm)
- Circular Fillet in 3D Space(III-3.htm)
- Ellipse in 3D Space(III-4.htm)
- Ellipse defined by Internal Rectangle(III-5.htm)
- Ellipse in 3D Space using Conjugate Diameters(III-6.htm)
- Tangents drawn to Ellipse(III-7.htm)
- Parabola in 3D Space through Three Points(III-8.htm)
- Bezier Parabola(III-9.htm)
- Bezier Parabola through Three Specified Points(III-10.htm)
- Hyperbola in 2D Space(III-11.htm)
- Shortest Distance from Point to Helix(III-12.htm)
- Shortest Distance from Point to 3rd Order Bezier Curve(III-13.htm)
- Bezier Surface of Revolution(III-14.htm)
- Intersection of 3D Lines(III-15.htm)
- Apparent Angle of Intersection between Two Lines(III-16.htm)
- Intersection of Line with Parametric Surface(III-17.htm)
- Shortest Distance from Point to 4th Order Bezier Curve(III-18.htm)
- Intersection between Bezier Curve and Hyperbola(III-19.htm)
- Cardioid in Polar Coordinates(III-20.htm)
- Intersection between Cardioid and Circle(III-21.htm)
- Intersection between Two Circles(III-22.htm)

Chapter 4: Curves and Surfaces

- Parabola and Hyperbola Intersection(IV-1.htm)
- Ruled Surface between Parabola and Hyperbola(IV-2.htm)
- Area, Centroid and Moment of Inertia Computations(IV-3.htm)
- Orthographic Projections of Surface(IV-4.htm)
- Ruled Surface between Circle and Ellipse(IV-5.htm)
- Parametric Quadric Surfaces(IV-6.htm)
- Surfaces of Revolution(IV-7.htm)
- Helical Surface(IV-8.htm)
- Surface Patch Derivatives on Unit Sphere(IV-9.htm)
- Gaussian and Average Curvature(IV-10.htm)
- Surface Area and Volume(IV-11.htm)
- Parametric Surface Mapping(IV-12.htm)
- Intersection of Line with Sphere(IV-13.htm)
- Geometric Properties of Paraboloid of Revolution(IV-14.htm)
- Intersection between Plane and Surface(IV-15.htm)
- Intersection between Plane and Cone(IV-16.htm)
- Sweep Surface with Axis Rotation(IV-17.htm)
- Sweep Surface with Circular Cross Section(IV-18.htm)
- Bezier Surface of Revolution about Vertical(IV-19.htm)
- Bezier Surface of Revolution about Horizontal(IV-20.htm)
- B-Spline Surface of Revolution(IV-21.htm)

- Piecewise Cubic Spline Interpolation(V-1.htm)
- Normalized Cubic Spline(V-2.htm)
- Relaxed End Condition(V-3.htm)
- Normalized Cubic Spline and Geometric Properties(V-4.htm)
- Chord Length Parameters(V-5.htm)
- Conic Bezier Curve(V-6.htm)
- Bezier Blending Functions(V-7.htm)
- Sixth Order Bezier Curve(V-8.htm)
- 3rd Order B-Spline Curve(V-9.htm)
- 2nd Order Open Uniform B-Spline(V-10.htm)
- 4th Order Open Uniform B-Spline(V-11.htm)
- 4th Order Periodic B-Spline(V-12.htm)
- Closed 4th Order Periodic B-Spline(V-13.htm)
- Periodic B-Spline of Airfoil Shape(V-14.htm)
- Closed 4th Order Non-Symmertical Periodic B-Spline(V-15)
- Matrix Formulation for Summetric B-Spline(V-16)
- Derivatives of 2nd Order Open Uniform B-Spline(V-17.htm)
- Derivatives of 4th Order Open Uniform B-Spline(V-18.htm)
- Five Vertex 2-D B-Spline Curve Fit(V-19.htm)
- B-Spline Curve Fit through 11 Points(V-20.htm)
- B-Spline Curve Fit through 9 Points(V-21.htm)
- B-Spline Curve Fairing(V-22.htm)
- Four Vertex Curve Fairing with Third Order Open Uniform B-Spline(V-23.htm)
- Regular and Rational 3rd Order B-Spline Curves(V-24.htm)
- 4th Order Regular and Rational B-Spline Curve(V-25.htm)
- 3rd Order Regular and Rational Periodic B-Spline Curves(V-26.htm)
- 4th Order Regular and Rational Periodic B-Spline Curves(V-27.htm)
- 2nd Order Open Rational Uniform B-Spline Derivatives(V-28.htm)
- 4th Order Open Uniform Derivatives(V-29.htm)
- 3rd Order Regular and Rational Open Uniform B-Spline Curves(V-30.htm)
- 3rd Order Non-Uniform Knot Vector for Rational Conics(V-31.htm)
- 3rd Order Non-Uniform Knot Vector for Closed Circle(V-32.htm)
- Quadratic Rational B-Spline Curve(V-33.htm)