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Front Cover
Solid Geometry with MATLAB Programming
Contents
Preface
1 Plane
1.1 Definition
1.2 General Equation of the First Degree in x, y, z Represents a Plane
1.3 Transformation of General form to Normal Form
1.4 Direction Cosines of the Normal to a Plane
1.5 Equation of a Plane Passing through a Given Point
1.6 Equation of the Plane in Intercept Form
1.7 Reduction of the General Equation of the Plane to the Intercept Form
1.8 Equation of a Plane Passing through three Points
1.9 Equation of any Plane Parallel to a Given Plane
1.10 Equation of Plane Passing through the Intersection of Two Given Planes
1.11 Equation of the Plane Passing through the Intersection
1.12 Angle between Two Planes
1.13 Position of the Origin w.r.t. the Angle between Two Planes
1.14 Two Sides of a Plane
1.15 Length of the Perpendicular from a Point to a Plane
1.16 Bisectors of Angles between Two Planes
1.17 Pair of Planes
1.18 Orthogonal Projection on a Plane
1.19 Volume of a Tetrahedron
Exercise
2 Straight Line
2.1 Representation of Line (Introduction)
2.2 Equation of a Straight Line in the Symmetrical Form
2.3 Equation of a Straight Line Passing through Two Points
2.4 Transformation from the Unsymmetrical to the Symmetrical Form
2.5 Angle between a Line and a Plane
2.6 Point of Intersection of a Line and a Plane
2.7 Conditions for a Line to Lie in a Plane
2.8 Condition of Coplanarity of Two Straight Lines
2.9 Skew Lines and the Shortest Distance between Two Lines
2.10 Equation of Two Skew Lines in Symmetric Form
2.11 Intersection of Three Planes
Exercise
3 Sphere
3.1 Definition
3.2 Equation of Sphere in Vector Form
3.3 General Equation of the Sphere
3.4 Equation of Sphere Whose End-Points of a Diameter are Given.
3.5 Equation of a Sphere Passing through the Four Points
3.6 Section of the Sphere by a Plane
3.7 Intersection of Two Spheres
3.8 Intersection of Sphere S and Line L
3.9 Tangent Plane
3.10 Equation of the Normal to the Sphere
3.11 Orthogonal Sphere
Exercise
4 Cone
4.1 Definition
4.2 Equation of a Cone with a Conic as Guiding Curve
4.3 Enveloping Cone to a Surface
4.4 Equation of the Cone whose Vertex is the Origin is Homogeneous
4.5 Intersection of a Line with a Cone
4.6 Equation of a Tangent Plane at (a, b, r) to the Cone with Vertex Origin
4.7 Conditions for Tangency
4.8 Right Circular Cone
Exercise
5 Cylinder
5.1 Definition
5.2 Equation of the Cylinder whose Generators Intersect the Given Conic
5.3 Enveloping Cylinder
5.4 Right Circular Cylinder
Exercise
6 Central Conicoid
6.1 Definition
6.2 Intersection of a Line with the Central Conicoid
6.3 Tangent Lines and Tangent Plane at a Point
6.4 Condition of Tangency
6.5 Normal to Central Conicoid
6.6 Plane of Contact
6.7 Polar Plane of a Point
Exercise
7 Miscellaneous Examples using MATLAB
Index
About the Authors
Back Cover.
Solid Geometry with MATLAB Programming
Contents
Preface
1 Plane
1.1 Definition
1.2 General Equation of the First Degree in x, y, z Represents a Plane
1.3 Transformation of General form to Normal Form
1.4 Direction Cosines of the Normal to a Plane
1.5 Equation of a Plane Passing through a Given Point
1.6 Equation of the Plane in Intercept Form
1.7 Reduction of the General Equation of the Plane to the Intercept Form
1.8 Equation of a Plane Passing through three Points
1.9 Equation of any Plane Parallel to a Given Plane
1.10 Equation of Plane Passing through the Intersection of Two Given Planes
1.11 Equation of the Plane Passing through the Intersection
1.12 Angle between Two Planes
1.13 Position of the Origin w.r.t. the Angle between Two Planes
1.14 Two Sides of a Plane
1.15 Length of the Perpendicular from a Point to a Plane
1.16 Bisectors of Angles between Two Planes
1.17 Pair of Planes
1.18 Orthogonal Projection on a Plane
1.19 Volume of a Tetrahedron
Exercise
2 Straight Line
2.1 Representation of Line (Introduction)
2.2 Equation of a Straight Line in the Symmetrical Form
2.3 Equation of a Straight Line Passing through Two Points
2.4 Transformation from the Unsymmetrical to the Symmetrical Form
2.5 Angle between a Line and a Plane
2.6 Point of Intersection of a Line and a Plane
2.7 Conditions for a Line to Lie in a Plane
2.8 Condition of Coplanarity of Two Straight Lines
2.9 Skew Lines and the Shortest Distance between Two Lines
2.10 Equation of Two Skew Lines in Symmetric Form
2.11 Intersection of Three Planes
Exercise
3 Sphere
3.1 Definition
3.2 Equation of Sphere in Vector Form
3.3 General Equation of the Sphere
3.4 Equation of Sphere Whose End-Points of a Diameter are Given.
3.5 Equation of a Sphere Passing through the Four Points
3.6 Section of the Sphere by a Plane
3.7 Intersection of Two Spheres
3.8 Intersection of Sphere S and Line L
3.9 Tangent Plane
3.10 Equation of the Normal to the Sphere
3.11 Orthogonal Sphere
Exercise
4 Cone
4.1 Definition
4.2 Equation of a Cone with a Conic as Guiding Curve
4.3 Enveloping Cone to a Surface
4.4 Equation of the Cone whose Vertex is the Origin is Homogeneous
4.5 Intersection of a Line with a Cone
4.6 Equation of a Tangent Plane at (a, b, r) to the Cone with Vertex Origin
4.7 Conditions for Tangency
4.8 Right Circular Cone
Exercise
5 Cylinder
5.1 Definition
5.2 Equation of the Cylinder whose Generators Intersect the Given Conic
5.3 Enveloping Cylinder
5.4 Right Circular Cylinder
Exercise
6 Central Conicoid
6.1 Definition
6.2 Intersection of a Line with the Central Conicoid
6.3 Tangent Lines and Tangent Plane at a Point
6.4 Condition of Tangency
6.5 Normal to Central Conicoid
6.6 Plane of Contact
6.7 Polar Plane of a Point
Exercise
7 Miscellaneous Examples using MATLAB
Index
About the Authors
Back Cover.