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Essential Mathematics for Computational Design in Grasshopper
Essential Mathematics for Computational Design in Grasshopper
Introduction (3:59)
Before your start, please review these recommendations: (2:39)
1. Vectors
1.1. Intro to Vectors (4:20)
1.2. Vector Representation (4:35)
1.3. Visualizing Vectors (4:26)
1.4. Position Vectors (7:19)
1.5. Vectors vs Points (2:11)
1.6. Vector Length and Unit Vector (3:45)
1.7. Quiz
1.8. Questions about Vectors?
2. Vector operations
2.1. Vector Scalar (6:01)
2.2. Vector Addition Operation (8:13)
2.3. Vector Subtraction Operation (12:27)
2.4. Summary of Basic Vector Operations (2:26)
2.5. Vector Dot Product Operation (8:46)
2.6. Vector Cross Product Operation (4:52)
2.7. Quiz
2.8. Questions about Vector Operations?
3. Vector Equations of Line and Plane
3.1. Vector Equation of a Line (14:13)
3.2. Points on a Line (8:25)
3.3. Vector Equation of a Plane (6:40)
3.4. Quiz
3.5. Questions about Line and Plane Equations?
Tutorial Session A: Vector Mathematics
A.1. Face Direction Tutorial
A.2. Exploded Box Tutorial
A.3. Tangent Spheres
4. Transformations
Introduction
4.1 Matrix Operations
4.2. Transformation Operations
4.2.1 Translation (Move) Transformation
4.2.2. Rotation transformation
4.2.3. Scale transformation
4.2.4. Shear transformation
4.2.5. Mirror or Reflection Transformation
4.2.6. Planar Projection Transformation
4.3. Quiz
4.4. Questions about Transformations?
5. Parametric Curves
5.1 Introduction to Parametric Curves (12:56)
5.2. Curve parameter
5.3. Curve Domain
5.4. Curve Evaluation
5.5. Tangent Vector to Curves
5.6. Cubic polynomial curves
5.7. Quiz
5.8.. Questions about Parametric Curves?
6. NURBS Curves
6.1. Introduction to NURBS Curves (9:00)
6.1.1. Degree
6.1.2. Control Points
6.1.3. Weights of Control Points
6.1.4. Knots
6.1.5. Evaluation Rule
6.2. Characteristics of NURBS Curves
6.3. Clamped vs. periodic NURBS curves
6.4. Weights
6.5. Evaluating NURBS Curves
6.6. Curve Geometric Continuity
6.7. Curve Curvature
6.8. Quiz
6.9. Questions about NURBS Curves?
7. Parametric Surfaces
7.1. Introduction to Parametric Surfaces
7.2. Surface Domain
7.3. Surface Evaluation
7.4. Tangent Plane of a Surface
7.5. Surface Geometric Continuity
7.6. Surface Curvature
7.7. Quiz
7.8. Questions about Parametric Surfaces?
8. NURBS Surfaces and Polysurfaces
8.1. Introduction to NURBS Surfaces
8.2. Characteristics of NURBS Surfaces
8.3. Singularity in NURBS Surfaces
8.4. Trimmed NURBS Surfaces
8.5. Polysurfaces
8.6. Quiz
8.7. Questions about NURBS Surfaces and Polysurfaces?
Tutorial Session B: Parametric Curves and Surfaces
B.1. Continuity Between Curves
B.2. Surfaces with Singularity
Conclusion and Feedback
Congratulations!
6.1.3. Weights of Control Points
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