Computer geometry and computer graphics algorithms. Computer geometry and computer graphics algorithms Nikulin computer graphics

The book details the mathematical and algorithmic foundations of modern computer graphics: models of graphic objects on a plane and in space (points, vectors, lines and surfaces, including composite, polyhedra, solid and voxel objects), geometric visualization tasks - a set of 2d- and 3d algorithms - cuts and removals, algorithms for affine and projective transformations, methods for depicting surfaces, including texturing. The material is accompanied a large number illustrations, block diagrams of algorithms and examples of their implementation. This manual is intended for students of the field of study "Informatics and Computer Engineering". It can also be useful for graduate students, university professors and all specialists, both comprehending the basics of computer graphics and developing new algorithms and applied graphics programs.
Vulture: Recommended by the Academic Council...

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Feedback from readers “Evgeny Nikulin: Computer graphics. Models and algorithms. Tutorial":

User Anatoly Tretyakov writes:

One of the most amazing stories I have ever read. Impregnated with love for art, ingenious and, accordingly, the most strange judgments that surprised and delighted.
Two twins are the closest people to each other, what can separate them? After all, they have been dividing the world since childhood.
A book about love, the pain that love causes, about kindred spirits, signs, ghosts of the past, "ghosts" and hope. We create our own destiny and find our own "ark" and Ralph))
If the previous book by this author, Sky Everywhere, didn’t hook me, then this one impressed me so much that I still return to it in my thoughts, and that means a lot.

The book provides the most complete presentation of the geometric and algorithmic foundations of modern computer graphics: mathematical models of graphic elements on a plane and in space, fundamental laws of geometric optics and algorithms for constructing optical effects based on them, methods of geometric transformations, analysis and synthesis of models of lines, surfaces and objects , geometric visualization problems - a set of 2d- and 3d-cutting and removal algorithms. The material is accompanied by a large number of illustrations, block diagrams of algorithms and examples of their implementation.

Publisher: BHV-Petersburg, 2005

ISBN 5-94157-264-6

Number of pages: 560.

Contents of the book "Computer Geometry and Computer Graphics Algorithms":

  • 1 Introduction
  • 5 Basic notation and relationships
  • 9 Chapter 1
    • 12 1.1. Graphic elements on the plane
      • 13 1.1.1. Models of a straight line on a plane
        • 13 1.1.1.1. Implicit equation of a straight line
        • 15 1.1.1.2. Normal equation of a straight line
        • 16 1.1.1.3. Parametric function of the straight line
        • 17 1.1.1.4. Equations of a straight line passing through two points
        • 18 1.1.1.5. Equations of a straight line in segments
      • 18 1.1.2. Mutual position of graphic elements on the plane
        • 18 1.1.2.1. Point Collinearity
        • 19 1.1.2.2. Mutual arrangement of lines
        • 19 1.1.2.3. Mutual position of a point and a line
        • 21 1.1.2.4. Construction of a straight line, the least distant from a set of points
        • 24 1.1.2.5. Intersection of two lines
        • 25 1.1.2.6. Line bundle equations and angle bisector
        • 27 1.1.2.7. Tests of properties of graphic elements on a plane
        • 32 1.1.2.8. Tests for point orientation relative to polygon
        • 42 1.1.2.9. Plane intersection algorithms
        • 48 1.1.2.10. Area and geometric center of a polygon
        • 51 1.1.2.11. Algorithms for generating random polygons
      • 54 1.1.3. Quadratic and parametric curves
    • 60 1.2. Graphic elements in space
      • 62 1.2.1. Plane models in space
        • 62 1.2.1.1. Implicit plane equation
        • 63 1.2.1.2. Normal plane equation
        • 64 1.2.1.3. Parametric plane function
        • 66 1.2.1.4. Equations of a plane passing through three points
        • 66 1.2.1.5. Plane equations in segments
        • 67 1.2.1.6. Line models in space
      • 69 1.2.2. Mutual position of graphic elements in space
        • 69 1.2.2.1. Point Collinearity
        • 69 1.2.2.2. Point coplanarity
        • 70 1.2.2.3. Point and line
        • 70 1.2.2.4. Point and plane
        • 71 1.2.2.5. Construction of the plane least distant from the set of points
        • 73 1.2.2.6. Mutual arrangement of two straight lines
        • 74 1.2.2.7. Mutual arrangement of a straight line and a plane
        • 75 1.2.2.8. two planes
        • 76 1.2.2.9. Plane bundle and bisector plane
        • 77 1.2.2.10. Plane intersection
        • 77 1.2.2.11. Polyhedron model
        • 80 1.2.2.12. Tests of properties of graphic elements in space
        • 83 1.2.2.13. Tests for the orientation of a point relative to a polyhedron
        • 85 1.2.2.14. Algorithms for intersection in space
      • 89 1.2.3. Quadratic and parametric surfaces
    • 99 1.3. Basic problems of geometric optics
      • 100 1.3.1. Intersection of a ray with a surface
      • 106 1.3.2. Reflection of a beam from a surface
      • 107 1.3.3. Refraction of the beam at the surface
      • 110 1.3.4. Forward and backward ray tracing
      • 112 1.3.5. Beam methods for constructing optical effects
        • 116 1.3.5.1. Shadow
        • 121 1.3.5.2. Reflection
        • 128 1.3.5.3. Refraction
  • 139 Chapter 2 Geometric Transformations
    • 140 2.1. Affine transformations
      • 140 2.1.1. Basic concepts and relationships
      • 144 2.1.2. Elementary affine transformations
        • 144 2.1.2.1. Transfer
        • 144 2.1.2.2. Scaling
        • 145 2.1.2.3. Shift
        • 148 2.1.2.4. Rotation
        • 149 2.1.2.5. Tabular calculation trigonometric functions
      • 154 2.1.3. Complex affine transformations
        • 155 2.1.3.1. Methods for calculating the complex transformation matrix
        • 170 2.1.3.2. Kinematic method of constructing objects
        • 182 2.1.3.3. Kinematic problem of movement in space
    • 194 2.2. Projective transformations
      • 196 2.2.1. Orthographic projections
      • 197 2.2.2. Axonometric projections
      • 207 2.2.3. oblique projections
      • 211 2.2.4. Central (perspective) projections
      • 221 2.2.5. Projective algorithms for complex transformations
        • 223 2.2.5.1. Projection of spatial lines onto a plane
        • 228 2.2.5.2. Stereographic projections
        • 231 2.2.5.3. Map projections
        • 242 2.2.5.4. Building a scene with a moving observer
        • 247 2.2.5.5. Projective algorithms for constructing optical effects
  • 201 Chapter 3. Mathematical models of surfaces and objects
    • 261 3.1. Surface modeling methods
      • 262 3.1.1. Surface rendering methods
        • 263 3.1.1.1. Image projection selection
        • 264 3.1.1.2. Frame surfaces
        • 268 3.1.1.3. Point surfaces
        • 271 3.1.1.4. Lighting Models and Shading Surfaces
      • 278 3.1 2. Kinematic surfaces
        • 282 3.1.2.1. Surfaces of revolution, transfer and combined
        • 289 3.1.2.2. Ruled surfaces and their developments
        • 307 3.1.2.3. Non-ruled surfaces
      • 324 3.1.3. Piecewise defined surfaces
      • 329 3.1.4. Splines
        • 330 3.1.4.1. Online Curves
        • 339 3.1.4.2. Spline surfaces
      • 347 3.1.5. Fractal Sets
        • 348 3.1.5.1. Mandelbrot fractal and algorithmic fractals
        • 353 3.1.5.2. geometric fractals
        • 370 3.1.5.3. Fractal Properties
      • 376 3.1.6. Graphic surfaces
    • 379 3.2. Models of objects in space
      • 381 3.2.1. Frame models. Platonic Solids
      • 393 3.2.2. Boundary Models
      • 395 3.2.3. solid models
  • 405 Chapter 4 Geometric Rendering Problems
    • 405 4.1. List Booleans
      • 408 4.1.1. Combining line lists
      • 411 4.1.2. Intersection of segment lists
      • 413 4.1.3. Excluding segment lists
    • 416 4.2. Clipping methods
      • 420 4.2.1. Regular Planar Clipping
      • 423 4.2.2. Arbitrary flat cutting of a segment
      • 429 4.2.3. Arbitrary flat clipping of a polygon
      • 432 4.2.4. Volumetric cutting of a segment
      • 434 4.2.5. Volume clipping of polygon and polyhedron
      • 442 4.2.6. Logical construction of 3d objects
      • 448 4.2.7. Additional tasks plane clipping
        • 448 4.2.7.1. Trimming a Convex Polygon with a Half-Plane
        • 452 4.2.7.2. Calculation of the core of an arbitrary polygon
        • 453 4.2.7.3. Convex polygon intersection
        • 454 4.2.7.4. Clipping the projection of a convex polygon
        • 461 4.2.7.5. Convex polygonal hull of point array
        • 464 4.2.7.6. Point Array Polygonalization
        • 468 4.2.7.7. Cutting a non-convex polygon
        • 472 4.2.7.8. Polygon triangulation
      • 484 4.2.8. Additional clipping tasks in space
        • 484 4.2.8.1. Cutting off a convex polyhedron by a half-space
        • 493 4.2.8.2. Section of a convex polyhedron by a plane
        • 495 4.2.8.3. Polyhedron core calculation
        • 496 4.2.8.4. Intersection of convex polyhedra
        • 498 4.2.8.5. Convex polyhedral hull of point array
    • 504 4.3. Removal Methods
      • 509 4.3.1. Preprocessing object models
        • 509 4.3.1.1. Choosing a World Coordinate System
        • 513 4.3.1.2. Constructing enclosing shells
        • 523 4.3.1.3. Face splitting
        • 530 4.3.1.4. Rejection of non-facial faces and normalization of vectors
      • 533 4.3.2. Removing Hidden Lines
      • 539 4.3.3. Hidden Edge Removal
  • 545 Conclusion
  • 549 Bibliography

The book details the mathematical and algorithmic foundations of modern computer graphics: models of graphic objects on a plane and in space (points, vectors, lines and surfaces, including composite, polyhedra, solid and voxel objects), geometric visualization tasks - a set of 2d- and 3d algorithms - cuts and removals, algorithms for affine and projective transformations, methods for depicting surfaces, including texturing. The material is accompanied by a large number of illustrations, block diagrams of algorithms and examples of their implementation. This manual is intended for students of the field of study "Informatics and Computer Engineering". It can also be useful for graduate students, university professors and all specialists, both comprehending the basics of computer graphics and developing new algorithms and applied graphics programs.
Vulture: Recommended by the Academic Council...

To download, select a format:

Feedback from readers “Evgeny Nikulin: Computer graphics. Models and algorithms. Tutorial":

User Andrey Belousov writes:

It was an abbreviated version. I guess, that full version books would not have mastered.
The main difficulty for me was the number of examples. Having got lost in endless examples, you often lose your train of thought, you have to go back and reread it. Some logical conclusions seem forced.
But on the other hand, this work is a cornerstone in religious studies, folklore. Yes, and in scientific atheism it is also referred to.
The book is not for entertainment and superficial reading, but for thoughtful unhurried reading.

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