CONTENTS
Introduction 1
1 Points and lines 5
1 Distance between Two Points 5
2 Equations of a Line 7
3 Distance from a Point to a Line 12
4 Angle between Two Lines 13
5 Intersection of Two Lines 16
6 Line through Two Points 19
7 Line Equidistant from Two Points 20
8 Normal to a Line through a Point 21
2 Points, lines and circles 23
1 Equations of a Circle 23
2 Intersections of a Line and a Circle 25
3 Intersections of Two Circles 27
4 Tangents from a Point to a Circle 29
5 Tangents to a Circle Normal to a Line 31
6 Tangents between Two Circles 33
7 Circles of Given Radius through Two Points 35
8 Circles of Given Radius through a Point and Tangent to a Line 36
9 Circles of Given Radius Tangent to Two Lines 38
10 Circles of Given Radius through a Point and Tangent to a Circle 40
11 Circles of Given Radius Tangent to a Line and a Circle 42
12 Circles of Given Radius Tangent to Two Circles 45
3 Points, line segments and arcs 46
1 Representation of a Line Segment 46
2 Distance from a Point to a Line Segment 47
3 Intersection of Two Line Segments 48
4 Representation of an Arc 53
5 Distance from a Point to an Arc 56
6 Intersections of a Line Segment and an Arc 58
7 Intersections of Two Arcs 61
4 Areas 62
1 Area of a Triangle 62
2 Centre of Gravity of a Triangle 63
3 Incentre of a Triangle 64
4 Circumcentre of a Triangle 65
5 Representation of a Polygon 66
6 Aorea of a Potygon 69
7 Centre of Gravity of a Polygon 70
8 Centre of Gravity of a Sector and Segment 72
5 Curves other than circles 74
1 General Implicit Quadratic Equations 74
2 Interpolation Using Geneial Implicit Quadratics 75
3 Parametric Polynomials 76
4 Interpolation Using Parametric Polynomials 77
5 Parametric Spline Curves 79
6 Radius of Curvature 82
6 Vectors, matrices and transformations 83
1 Vectors 83
2 Matrices 86
3 Determinants 87
4 Transformations 88
5 Perspective 90
7 Points, lines and planes 96
1 Distance between Two Points in Space 96
2 Equations of a Straight Line in Space 97
3 Distance from a Point to a Line in Space 98
4 Distance between Two Lines in Space 100
5 Angle between Two Lines in Space 101
6 Line through Two Points in Space 103
7 Equation of a Plane 104
8 Distance from a Point to a Plane 107
9 Angle between a Line and a Plane 108
10 Angle between two Planes 110
11 Intersection of a Line and a Plane 111
12 Intersection of Three Planes 112
13 Intersection of Two Planes 113
14 Plane through Three Points 114
15 Plane tirough a Point and Normal to a Line 116
16 Plane through Two Points and Parallel to a Line 116
8 Volumes 118
1 Volume of a Tetrahedron 118
2 Centre of Gravity and Surface Area of a Tetrahedron 119
3 Circumcentre of a Tetrahedron 120
4 Volume and Surface Area of a Cylinder and of a Sphere 122
5 Volume and Centre of Gravity of a Sector of a Sphere 123
6 Volume, Surface Area and Centre of Gravity of a Cone 124
9 Drawing pictures 126
1 Line and Pixel Devices 126
2 Circles on Line Devices 127
3 Arcs on Line Devices 129
4 Lines on Pixel Devices 130
5 Circles on Pixel Devices 131
6 Clipping 133
References 138