Vectors and Planes vs Geometry Visualization

Vectors and Planes App helps visualize and understand 3D linear and quadric structures and their intersections. List of linear structures and combinations: 1. Two vector combination. 2. Plane. 3. Line and plane combination. 4. Two plane combination. 5. Three plane combination. Current list of quadric structures: 1. Two sphere combination. 2. Standard ellipsoid. 3. Ellipsoid in a form of positive-definite matrix. 4. Standard cone. 5. Cone in a form of indefinite matrix. 6. 1-sheet hyperboloid. 7. 1-sheet hyperboloid in a form of indefinite matrix. 8. 2-sheet hyperboloid. 9. 2-sheet hyperboloid in a form of indefinite matrix. 10. Standard cylinder. 11. Cylinder in a form of positive-semidefinite matrix. 12. Hyperbolic paraboloid. 13. Elliptic paraboloid. Current list of combinations of quadric and linear structures: 1. Matrix ellipsoid and line. 2. Standard ellipsoid and plane. 3. Matrix ellipsoid and plane. 4. Matrix cone and line. 5. Standard cone and plane. 6. 1-sheet hyperboloid in matrix form and line. 7. 2-sheet hyperboloid in matrix form and line. 8. Matrix cylinder and line. 9. Elliptic paraboloid and line. 10. Hyperbolic paraboloid and line. Interactive 3D graphs are provided for all of the above. Step by step calculation algorithms are provided for all intersection point sets. Many of the algorithms are based on Linear Algebra concepts. Those, in turn, are explained in our “Matrix Solver Step by Step” app. Version 10 was completely redesigned. Developers hope to get feedback from users at graphmath@aol.com.

Understand 3D Orientation. See It in Real Time. This app is a hands-on visualization tool designed for developers working with SceneKit. It helps you clearly understand how pitch, yaw, and roll interact — and how material order affects rendering on standard 3D geometries. Whether you're learning 3D graphics, debugging orientation issues, or experimenting with material stacks, this app provides a clean, interactive environment for exploration. Explore 3D Orientation • Adjust pitch, yaw, and roll independently • Observe how rotation order affects final orientation • See real-time updates as values change • Build intuition for 3D transform behavior Standard SceneKit Geometries; Visualize common primitives such as: • Box • Sphere • Cylinder • Cone • Capsule • Plane • Other standard SceneKit shapes Understand Material Application • Explore how materials are applied to geometry elements • See how material order impacts rendering • Experiment with multi-material configurations • Better understand SceneKit’s material indexing Built for Developers • Ideal for iOS and macOS developers working with SceneKit • Great companion tool for learning 3D math concepts • Useful for debugging transform and rendering behavior • Clean, distraction-free interface focused on learning If you work with SceneKit, 3D transforms, AR, or graphics programming, this app helps you see what the math is doing.