Essential Mathematics for Computer Graphics Fast,9781852333805

Essential Mathematics for Computer Graphics Fast

by
ISBN13: 9781852333805
ISBN10: 1852333804
Format: Paperback
Pub. Date: 2001-10-01
Publisher(s): Springer-Verlag New York Inc
Upgraded Edition: Click here!
  • Free Shipping Icon

    This Item Qualifies for Free Shipping!*

    *Excludes marketplace orders.

List Price: $36.70

Rent Book

Select for Price
Add to Cart
There was a problem. Please try again later.

Rent Digital

Rent Digital Options
Online:30 Days access
Downloadable:30 Days
$32.04
Online:60 Days access
Downloadable:60 Days
$42.72
Online:90 Days access
Downloadable:90 Days
$53.40
Online:120 Days access
Downloadable:120 Days
$64.08
Online:180 Days access
Downloadable:180 Days
$69.42
Online:1825 Days access
Downloadable:Lifetime Access
$106.80
$69.42
Add to Cart

New Book

We're Sorry
Sold Out

Used Book

We're Sorry
Sold Out

Buy from our Marketplace starting at $45.77

How Marketplace Works:

  • This item is offered by an independent seller and not shipped from our warehouse
  • Item details like edition and cover design may differ from our description; see seller's comments before ordering.
  • Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
  • Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
  • Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.

Summary

Baffled by maths? Then don't give up hope.John Vince will show you how to understand many of the mathematical ideas used in computer animation, virtual reality, CAD, and other areas of computer graphics.In ten chapters you will rediscover - and hopefully discover for the first time a new way of understanding - the mathematical techniques required to solve problems and design computer programs for computer graphic applications. Each chapter explores a specific mathematical topic and takes you forward into more advanced areas until you are able to understand 3D curves and surface patches, and solve problems using vectors.After reading the book, you should be able to refer to more challenging books with confidence and develop a greater insight into the design of computer graphics software.Get to grips with mathematics fast ...- Numbers- Algebra- Trigonometry- Coordinate geometry- Transforms- Vectors- Curves and surfaces- Analytic geometryEssential Mathematics for Computer Graphics fastThe book you will read once, and refer to over and over again!

Table of Contents

Mathematics
1(6)
Is Mathematics difficult?
3(1)
Who should read this book?
4(1)
Aims and objectives of this book
4(1)
Assumptions made in this book
5(1)
How to use the book
5(2)
Numbers
7(8)
Natural numbers
8(1)
Prime numbers
8(1)
Integers
9(1)
Rational numbers
9(1)
Irrational numbers
10(1)
Real numbers
10(1)
The number line
10(1)
Complex numbers
10(3)
Summary
13(2)
Algebra
15(10)
Notation
16(1)
Algebraic laws
17(2)
Associative law
18(1)
Commutative law
18(1)
Distributive law
19(1)
Solving the roots of a quadratic equation
19(1)
Indices
20(1)
Laws of indices
21(1)
Examples
21(1)
Logarithms
21(2)
Further notation
23(1)
Summary
23(2)
Trigonometry
25(8)
The trigonometric ratios
26(2)
Example
28(1)
Inverse trigonometric ratios
28(1)
Trigonometric relationships
29(1)
The sine rule
29(1)
The cosine rule
30(1)
Compound angles
30(1)
Perimeter relationships
31(1)
Summary
32(1)
Cartesian Coordinates
33(10)
The Cartesian xy-plane
34(6)
Function graphs
36(1)
Geometric shapes
37(1)
Polygonal shapes
37(1)
Areas of shapes
38(1)
Theorem of Pythagoras in 2D
39(1)
3D coordinates
40(2)
Theorem of Pythagoras in 3D
40(1)
3D polygons
41(1)
Euler's rule
41(1)
Summary
42(1)
Vectors
43(26)
2D vectors
45(4)
Vector notation
45(1)
Graphical representation of vectors
45(2)
Magnitude of a vector
47(2)
3D vectors
49(16)
Vector manipulation
49(1)
Multiplying a vector by a scalar
50(1)
Vector addition and subtraction
50(1)
Position vectors
51(1)
Unit vectors
52(1)
Cartesian vectors
53(1)
Vector multiplication
54(1)
Scalar product
55(2)
Example of the dot product
57(1)
The dot product in lighting calculations
58(1)
The dot product in back-face detection
59(1)
The vector product
60(4)
The right-hand rule
64(1)
Deriving a unit normal vector for a triangle
65(1)
Areas
66(2)
Calculating 2D areas
67(1)
Summary
68(1)
Transformations
69(60)
2D transformations
70(2)
Translation
70(1)
Scaling
70(1)
Reflection
71(1)
Matrices
72(5)
Systems of notation
75(1)
The determinant of a matrix
76(1)
Homogeneous coordinates
77(12)
2D translation
79(1)
2D scaling
79(1)
2D reflections
80(2)
20 shearing
82(1)
2D rotation
83(3)
2D scaling
86(1)
2D reflections
87(1)
2D rotation about an arbitrary point
88(1)
3D transformations
89(9)
3D translation
89(1)
3D scaling
90(1)
3D rotations
90(5)
Gimbal lock
95(1)
Rotating about an axis
96(2)
3D reflections
98(1)
Change of axes
98(22)
2D change of axes
99(1)
Direction cosines
100(2)
Positioning the virtual camera
102(1)
Direction cosines
103(3)
Euler angles
106(4)
Quaternions
110(1)
Adding and subtracting quaternions
110(1)
Multiplying quaternions
111(1)
The inverse quaternion
111(1)
Rotating points about an axis
112(4)
Roll, pitch and yaw quaternions
116(2)
Quaternions in matrix form
118(1)
Frames of reference
119(1)
Transforming vectors
120(2)
Determinants
122(4)
Perspective projection
126(2)
Summary
128(1)
Interpolation
129(20)
Linear interpolation
130(3)
Non-linear interpolation
133(8)
Trigonometric interpolation
133(2)
Cubic interpolation
135(6)
Interpolating vectors
141(4)
Interpolating quaternions
145(2)
Summary
147(2)
Curves and Patches
149(32)
The circle
150(1)
The ellipse
151(1)
Bezier curves
152(10)
Bernstein polynomials
152(5)
Quadratic Bezier curves
157(1)
Cubic Bernstein polynomials
158(4)
A recursive Bezier formula
162(1)
Bezier curves using matrices
162(5)
Linear interpolation
164(3)
B-splines
167(6)
Uniform B-splines
168(3)
Continuity
171(1)
Non-uniform B-splines
172(1)
Non-uniform Rational B-Splines
172(1)
Surface patches
173(7)
Planar surface patch
173(1)
Quadratic Bezier surface patch
174(3)
Cubic Bezier surface patch
177(3)
Summary
180(1)
Analytic Geometry
181(40)
Review of geometry
182(11)
Angles
182(1)
Intercept theorems
183(1)
Golden Section
184(1)
Triangles
185(1)
Center of gravity of a triangle
185(1)
Isosceles triangle
186(1)
Equilateral triangle
187(1)
Right triangle
187(1)
Theorem of Thales
187(1)
Theorem of Pythagoras
188(1)
Quadrilateral
188(1)
Trapezoid
189(1)
Parallelogram
189(1)
Rhombus
190(1)
Regular polygon (n-gon)
190(2)
Circle
192(1)
2D analytic geometry
193(6)
Equation of a straight line
193(1)
The Hessian normal form
194(3)
Space partitioning
197(1)
The Hessian normal form from two points
198(1)
Intersection points
199(3)
Intersection point of two straight lines
199(1)
Intersection point of two line segments
199(3)
Point inside a triangle
202(5)
Area of a triangle
202(3)
Hessian normal form
205(2)
Intersection of a circle with a straight line
207(2)
3D geometry
209(9)
Equation of a straight line
209(2)
Point of intersection of two straight lines
211(4)
Equation of a plane
215(1)
Space partitioning
216(1)
Point of intersection of a line and a plane
216(2)
Point of intersection of a line segment and a plane
218(1)
Summary
219(2)
Conclusion
221(2)
References 223(2)
Index 225

An electronic version of this book is available through VitalSource.

This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.

By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.

Digital License

You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.

More details can be found here.

A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.

Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.

Please view the compatibility matrix prior to purchase.