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C∞ Continuity
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Classroom Contents
The Continuity of Splines
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- 1 Intro
- 2 Examples of Paths
- 3 CHAPTER 1 - Bézier Curves
- 4 Lerp
- 5 Quadratic Bézier
- 6 Cubic Bézier
- 7 n-Degree Bézier
- 8 CHAPTER 2 - Bézier Splines
- 9 Cubic Bézier Spline
- 10 Spline Parameterization
- 11 The Anatomy of a Spline
- 12 Knot Values & Knot Intervals
- 13 Local Control
- 14 The flexibility of the Cubic Bézier
- 15 Tangent Points
- 16 CHAPTER 3 - Continuity
- 17 C⁰ Positional Continuity
- 18 Spline Derivatives
- 19 C¹ Velocity Continuity
- 20 C² Acceleration Continuity
- 21 Cascading Loss of Local Control
- 22 C³ Jolt Continuity
- 23 C∞ Continuity
- 24 Parametric Continuity Summary
- 25 CHAPTER 4 - Geometric Continuity
- 26 G¹ Tangent Continuity
- 27 G² Curvature Continuity
- 28 The Reflection Test
- 29 Seams in Circular Arcs
- 30 Angle Analysis
- 31 Curvature & The Osculating Circle
- 32 Curvature Combs
- 33 G¹ Algebraically
- 34 G² Algebraically
- 35 Geometric Continuity Summary
- 36 Continuity Summarized
- 37 Cusps
- 38 CHAPTER 5: The Extended Universe
- 39 Hermite Spline
- 40 Hermite ⇔ Bézier Conversion
- 41 Linear Spline
- 42 Cardinal Spline
- 43 Catmull-Rom Spline
- 44 Investigating Basis Functions
- 45 Basis Function Continuity Analysis
- 46 In Search of a C² Spline
- 47 B-Spline
- 48 Quiz Time!
- 49 Cubic Trajectory
- 50 Uniform Cubic Splines
- 51 Splines & Their Use Cases
- 52 Outro
- 53 NURBS
- 54 Color Spline
- 55 Credits & Freya Rambles
- 56 Cats helping me w. recording
