C program for 2. D Transformations#include< stdio. Programming 2. D Computer Graphics . Discover the basics of 2. D graphics programming and how easy the formulas are to use. This chapter is from the book . These functions hide many programming. Still, to. understand Direct. D, you need to have a little background in standard 3. D. programming practices. The first step toward that goal is to understand how your. D images. This chapter, then, introduces you to the basics of 2. D graphics programming. D. shapes in various ways. Although transforming 2. D shapes requires that you know a. In this chapter, you learn: About screen and Cartesian coordinates. About using vertices to define 2. D shapes. About translating, scaling, and rotating 2. D shapes. How to use matrices to transform 2. D shapes. Undoubtedly, you have at least some minimal experience with drawing images on. Windows. For example, you probably know that to draw a. GDI function Move. To. Ex() to position. Line. To() to. draw the line. To write a C program to draw a line using Bresenham’s Algorithm. COMPUTER GRAPHICS LABORATORY PROGRAM . Implementation of 3D Transformation in Computer Graphics To write a C program to implement 3D transformations. 3 Dimensional Transformation. 3D 2D Translation, Computer Graphics lab. Two Dimensional Transformation CHAPTER 2. Geometric Modeling provides a mathematical description of a geometric object. Using the matrix equation for translation. In a program, those two function calls would look something like. Move. To. Ex(h. DC, x, y, 0). Line. To(h. DC, x, y); The arguments for the Move. To. Ex() function are a handle to a device context. DC), the X,Y coordinates of the point in the window to which you want to move. POINT structure in which the function should store the. If this last argument is 0. Move. To. Ex() doesn't supply the current position. The arguments for the. Line. To() function are a handle to a DC and the X,Y coordinates of the end of the. Of interest here are the X,Y coordinates used for the end points that define. Assuming the default mapping mode of MM. Figure. 3. 1 shows this coordinate system. Figure. 3. 1 A window's MM. Unfortunately, most objects. Cartesian coordinate system. COMPUTER GRAPHICS LAB MANUAL October 1, 2011. Calculate the initial value of the decision parameter in region 2 using the last point. To write a C program to perform 2D composite transformations. This is an introduction to 2D and 3 in computer graphics presented by daroko blog. Y coordinates so that they increase as you move up from the. Also, as shown in Figure 3. Cartesian coordinate system allows negative coordinates. If you remember. any of your high school math, you'll recognize Figure. In computer graphics, however. Cartesian plane as a surface that represents the world in. Figure. 3. 2 The Cartesian coordinate system. You define graphical objects in the Cartesian coordinate system by specifying. For example, a triangle can be defined. Figure 3. 3. As you can see by Figure. Y coordinates. in the screen's coordinate system as compared with the Cartesian coordinate. The C++ code that produces the triangle looks like this: Move. To. Ex(h. DC, 2, 5, 0). Line. To(h. DC, 5, 2). Line. To(h. DC, 2, 2). Line. To(h. DC, 2, 5); Figure. Drawing a triangle with no mapping between the Cartesian. Because of the differences between a screen display and the Cartesian. In graphics terms, you must map points in the Cartesian coordinate. Forgetting about negative coordinates for the. Cartesian coordinate system to point. C++ program code: x. Y - y. 1; Because the X coordinate is unaffected by the mapping, x. To reverse the Y coordinate, the original Y coordinate is. Y coordinate. Of course, for this. You can get this. Windows API function Get. Client. Rect(), which fills a RECT. Listing 3. 1 draws a. Cartesian coordinates and the screen. Listing 3. 1 Drawing a Triangleint triangle. Later in this chapter, you develop a complete Windows program. In the preceding code, the first line defines an array that contains the. Cartesian coordinates of the triangle. The variables new. X and. new. Y will hold the screen coordinates for a point, and the variables. X and start. Y will hold the screen coordinates for the. The RECT structure, client. Rect. will hold the size of the window's client area. After declaring the local variables, the code calls Get. Client. Rect(). to fill in the client. Rect structure, at which point the. The code assigns this value to the local variable. Y. A for loop then iterates through the triangle's coordinate. Inside the loop, the currently indexed X,Y coordinates are mapped from. Cartesian coordinates to screen coordinates. The first mapped point is used to. The code uses subsequent points to draw. The call to Line. To() outside the.
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MATH 1. 00. 0 or MATH 1. MPP score of 0. 48 or MPA2 score of 0. MPME score of 0. 52. Basic analytic and geometric rties of trigonometric functions. Complex numbers, De Moivre's Theorem, polar coordinates. No credit is given to students with higher- numbered math course. Credit for only one of MATH 1. MATH 1. 12. 3. MATH 1. PRE- CALCULUS TRIGONOMETRY (3) LEC. A0. 2 score of 2. S0. 2 score of 5. MATH 1. 12. 0 or MATH 1. MPP score of 0. 56 or MPA2 score of 0. MPME score of 0. 60. Students may receive credit for only one of MATH 1. MATH 1. 13. 3. MATH 1. PRE- CALCULUS ALGEBRA AND TRIGONOMETRY (4) LEC. A0. 2 score of 2. S0. 2 score of 5. MPP score of 0. 64 or MPA2 score of 0. MATH 1. 00. 0 or MATH 1. MPME score of 0. 60. Algebraic functions, Exponential Logarithmic functions. Analytic and geometric properties of trigonometric functions. Students may receive credit for only one of MATH 1. MATH 1. 15. 3. MATH 1. MATHEXCEL PRECALCULUS WORKSHOP (2) LEC. Appropriate score on the mathematics placement exam or grade of C or better in MATH 1. Workshop for MATH 1. Fall, Spring. MATH 1. CALCULUS I (4) LEC. A0. 2 score of 2. S0. 2 score of 6. MPQ score of 1. 00 and MPP score of 0. MPQ score of 1. 00 and MPA2 score of 0. MATH 1. 13. 0 or MATH 1. MATH 1. 15. 0 or MATH 1. MATH 1. 13. 0 or MPME score of 0. Applications of the derivative, antiderivatives, the definite integral and applications to area problems, the fundamental theorem of calculus. Workshop for MATH 1. Students may receive credit for only one of MATH 1. MATH 1. 61. 7, or MATH 1. MATH 1. 62. 0/1. 62. CALCULUS II (4) LEC. MATH 1. 61. 0 or MATH 1. MATH 1. 61. 7 or MATH 1. MATH 1. 61. 0. Techniques of integration, applications of the integral, parametric equations, polar coordinates. Students may receive credit for only one of MATH 1. MATH 1. 62. 7, or MATH 1. MATH 1. 62. 1 MATHEXCEL CALCULUS WORKSHOP II (2) LEC. Workshop for MATH 1. The same material as MATH 1. A0. 2 score of 2. S0. 2 score of 5. MATH 1. 12. 0 or MATH 1. MATH 1. 13. 0 or MATH 1. MATH 1. 15. 0 or MATH 1. MPP score of 0. 72 or MPA2 score of 0. MPME score of 0. 68. Students in College of Business. Differentiation and integration of exponential and logarithmic functions, applications to business. Functions of several variables, partial derivatives, multiple integrals. MATH 1. 68. 1 MATHEXCEL BUSINESS CALCULUS WORKSHOP I (2) LEC. Workshop for MATH 1. MATH 1. 68. 0 or MATH 1. MATH 1. 61. 0 or MATH 1. MATH 1. 61. 3 or Departmental approval. Probability, random variables, probability distributions. Further topics in calculus: integration, functions of several variables, applications to probability. Applications to business and related areas. Workshop for MATH 1. A0. 2 score of 2. S0. 2 score of 6. MATH 1. 13. 0 or MATH 1. MATH 1. 15. 0 or MATH 1. MATH 1. 13. 0 or MPME score of 0. Credit will be given for only only one of MATH 1. Credit will not be given for MATH 1. MATH 1. 71. 0. MATH 1. MATH 1. 72. 0 include and re- order the material of MATH 1. MATH 1. 62. 0, and MATH 1. MATH 1. 72. 0 CALCULUS FOR ENGINEERING AND SCIENCE II (4) LEC. Exponents and logarithms, separation of variables, L'Hopital's rule. Techniques of integration, work and energy, line integrals, the gradient and directional derivatives, the curl. MATH 1. 62. 0 or MATH 1. MATH 1. 72. 0 or MATH 1. MATH 1. 62. 3. Multivariate calculus: vector- valued functions, partial derivatives, multiple integration, vector calculus. Credit will be given for only one of MATH 2. MATH 2. 63. 7, or MATH 2. MATH 2. 63. 7 HONORS CALCULUS III (4) LEC. The same material as MATH 2. P/C MATH 2. 63. 0 or P/C MATH 2. P/C MATH 2. 73. 0. First and second order linear differential equations including the solutions by infinite series, applications. MATH 2. 66. 0 TOPICS IN LINEAR ALGEBRA (3) LEC. MATH 1. 62. 0 or MATH 1. MATH 1. 62. 7 or MATH 1. 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Similarities, congruences and transformations. For Elementary Education majors or by. MATH 2. 87. 0 MATHEMATICS FOR ELEMENTARY EDUCATION III (3) LEC. Departmental approval. Mathematical insights into probability, data analysis and functions for elementary school teachers. Uncertainty, probability spaces and an introduction to statistics. Relationships, functions and change. For Elementary Education majors or by. MATH 3. 01. 0 HISTORY OF MATHEMATICS (3) LEC. MATH 1. 62. 0 or MATH 1. MATH 1. 62. 7 or MATH 1. Departmental approval. The evolution of modern mathematics from its motivational roots in the physical sciences; the lives and contributions of outstanding mathematicians; the parallel development of mathematics and western culture. MATH 3. 10. 0 INTRODUCTION TO ADVANCED MATHEMATICS (3) LEC. MATH 2. 63. 0 or MATH 2. MATH 2. 73. 0. Teaching of the fundamental abilities necessary for the pursuance of mathematical studies. Logic and set theory, mathematical induction, basic number theory, basic analysis. Methods of proof, induction, counting, inclusion- exclusion, discrete probability, relations, partial orders, graphs, trees, languages, grammars, finite state machines, automata. MATH 2. 63. 0 or MATH 2. MATH 2. 73. 0. Advanced topics in logic. For example: soundness, completeness, incompleteness, set theory, proof theory, odel theory, non- standard logics. Intensive seminar in the mathematical aspects of finance, and the theory of interest primarily intended as preparation for the Society of Actuaries Course 2 examination. MATH 4. 82. 0 ACTUARIAL SEMINAR IN PROBABILITY (3) LEC. Intensive seminar in calculus, probability, and risk theory primarily intended as preparation for the Society of Actuaries Course 1 examination. MATH 4. 93. 0 DIRECTED STUDIES (1- 3) IND. Study of individual problems or topics of interest to students. Course may be repeated for a maximum of 3 credit hours. MATH 4. 97. 0 SPECIAL TOPICS (1- 4) IND. Departmental approval. An individual problems course. Course may be repeated for a maximum of 4 credit hours. MATH 4. 98. 0 UNDERGRADUATE RESEARCH (1- 3) IND. Departmental approval. Directed research in the area of specialty under faculty supervison. Course may be repeated for a maximum of 3 credit hours. MATH 4. 99. 7 HONORS THESIS (1- 6) IND. Honors College Course may be repeated for a maximum of 6 credit hours. Membership in Honors College. MATH 5. 00. 0 MATH MODELING CONTINUOUS (3) LEC. MATH 2. 65. 0 and MATH 2. Introduction to mathematical models and related techniques. Includes general principles involving continuous deterministic problems and a detailed, specific term project. Departmental approval. Vector- valued functions, vector fields. Gradient, divergence, curl. Integral theorems: Green's Theorem, Stoke's Theorem, Gauss' Theorem. Tensors and differential forms. Applications. MATH 5. COMPLEX VARIABLES WITH APPLICATIONS I (3) LEC. Complex functions and their elementary mapping properties; contour integration and residues; Laurent series; applications to real integrals. Linear fractional transformations; conformal mappings; harmonic functions; applications to boundary value problems; analytic continuation; entire functions. MATH 5. 03. 0- 5. MATH 5. 05. 0 MATRIX THEORY AND APPLICATIONS (3) LEC. Canonical forms, determinants, linear equations, eigenvalue problems. MATH 5. 06. 0 ELEMENTARY PARTIAL DIFFERENTIAL EQUATIONS (3) LEC. First and second order linear partial differential equations with emphasis on the method of eigenfunction expansions. MATH 5. 12. 0 INFORMATION THEORY (3) LEC. MATH 2. 63. 0 or MATH 2. MATH 2. 73. 0. Information and entropy, information rate optimization and channel capacity, variable- length codes, data compression (Kraft- Mc. Millan inequality, Huffman's algorithm), maximum likelihood decoding, Shannon's Noisy Channel Theorem. MATH 5. 13. 0 CALCULUS OF VARIATION (3) LEC. Fundamental concepts of extrema of functions and functionals; first and second variations; generalizations; sufficient conditions; constrained functionals; the general Lagrange Problem; optimal control. MATH 5. 14. 0 DATA COMPRESSION (3) LEC. MATH 1. 62. 0 or MATH 1. MATH 1. 62. 7 or MATH 1. Lossless compression methods, including static, dynamic, and higher order Huffman and arithmetic encoding, interval and recency rank encoding, and dictionary methods; lossy transform methods (JPEG). MATH 5. 15. 0 ALGEBRAIC CODING THEORY (3) LEC. Linear codes, Hamming and Golay codes, BCH codes, cyclic codes. Random error detection and correction. Burst- error correction. MATH 2. 65. 0 and MATH 2. |
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