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3.5. LINE SEGMENTS 230 3.5 Line Segments A line segment results from a line strip Begin / End object, a line loop, or a series of separate line segments. Line segment rasterization is controlled by several variables. Line width, which may be set by calling void LineWidth( float width ); with an appropriate positive floating-point width, controls the width of rasterized line segments. The default width is 1.0. Values less than or equal to 0.0 generate the error INVALID_VALUE. Antialiasing is controlled with Enable and Disable using the symbolic constant LINE_SMOOTH. Finally, line segments may be stippled. Stippling is controlled by a GL command that sets a stipple pattern (see below). 3.5.1 Basic Line Segment Rasterization Line segment rasterization begins by characterizing the segment as either x-major or y-major. x-major line segments have slope in the closed interval [−1, 1]; all other line segments are y-major (slope is determined by the segment’s endpoints). We shall specify rasterization only for x-major segments except in cases where the modifications for y-major segments are not self-evident. Ideally, the GL uses a “diamond-exit” rule to determine those fragments that are produced by rasterizing a line segment. For each fragment f with center at window coordinates x f and y f , define a diamond-shaped region that is the intersection of four half planes: R f = { (x, y) | |x − x f | + |y − y f | < 1/2.} Essentially, a line segment starting at p a and ending at p b produces those fragments f for which the segment intersects R f , except if p b is contained in R f . See figure 3.4. To avoid difficulties when an endpoint lies on a boundary of R f we (in principle) perturb the supplied endpoints by a tiny amount. Let p a and p b have window coordinates (x a , y a ) and (x b , y b ), respectively. Obtain the perturbed endpoints p ′ a given by (x a , y a ) − (ɛ, ɛ 2 ) and p ′ b given by (x b, y b ) − (ɛ, ɛ 2 ). Rasterizing the line segment starting at p a and ending at p b produces those fragments f for which the segment starting at p ′ a and ending on p ′ b intersects R f , except if p ′ b is contained in R f . ɛ is chosen to be so small that rasterizing the line segment produces the same fragments when δ is substituted for ɛ for any 0 < δ ≤ ɛ. When p a and p b lie on fragment centers, this characterization of fragments reduces to Bresenham’s algorithm with one modification: lines produced in this OpenGL 4.2 (Compatibility Profile) - August 22, 2011
¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ 3.5. LINE SEGMENTS 231 © © © © © © © © © © © © © © © © © © © © ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¡ ¡ ¡ ¡ § § § § § ¡ ¡ ¡ ¡ ¡ § § § § § ¡ ¡ ¡ ¡ ¡ § § § § § ¡ ¡ ¡ ¡ ¡ § § § § § ¡ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ £ £ £ £ ¤ ¤ ¤ ¤ ¤ ¥ ¥ ¥ ¥ ¥ £ £ £ £ £ ¤ ¤ ¤ ¤ ¤ ¥ ¥ ¥ ¥ ¥ £ £ £ £ £ ¤ ¤ ¤ ¤ ¤ ¥ ¥ ¥ ¥ ¥ £ £ £ £ £ ¤ ¤ ¤ ¤ ¤ ¥ ¥ ¥ ¥ ¥ £ Figure 3.4. Visualization of Bresenham’s algorithm. A portion of a line segment is shown. A diamond shaped region of height 1 is placed around each fragment center; those regions that the line segment exits cause rasterization to produce corresponding fragments. description are “half-open,” meaning that the final fragment (corresponding to p b ) is not drawn. This means that when rasterizing a series of connected line segments, shared endpoints will be produced only once rather than twice (as would occur with Bresenham’s algorithm). Because the initial and final conditions of the diamond-exit rule may be difficult to implement, other line segment rasterization algorithms are allowed, subject to the following rules: 1. The coordinates of a fragment produced by the algorithm may not deviate by more than one unit in either x or y window coordinates from a corresponding fragment produced by the diamond-exit rule. 2. The total number of fragments produced by the algorithm may differ from that produced by the diamond-exit rule by no more than one. 3. For an x-major line, no two fragments may be produced that lie in the same window-coordinate column (for a y-major line, no two fragments may appear in the same row). 4. If two line segments share a common endpoint, and both segments are either x-major (both left-to-right or both right-to-left) or y-major (both bottom-to- OpenGL 4.2 (Compatibility Profile) - August 22, 2011
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The OpenGL R○ Graphics System: A
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Contents 1 Introduction 1 1.1 Forma
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CONTENTS iii 2.15 Tessellation . .
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CONTENTS v 3.12 Fog . . . . . . . .
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CONTENTS vii A Invariance 579 A.1 R
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CONTENTS ix L Version 4.2 649 L.1 N
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CONTENTS xi M.3.70 BPTC texture com
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LIST OF FIGURES xiii 3.11 Example o
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LIST OF TABLES xv 3.10 UNSIGNED_SHO
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LIST OF TABLES xvii 6.29 Pixel Oper
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Chapter 1 Introduction This documen
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1.5. OUR VIEW 3 available to the us
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Chapter 2 OpenGL Operation 2.1 Open
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2.1. OPENGL FUNDAMENTALS 7 section
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2.1. OPENGL FUNDAMENTALS 9 must not
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2.1. OPENGL FUNDAMENTALS 11 2.1.2 F
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2.3. GL COMMAND SYNTAX 13 describe
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2.3. GL COMMAND SYNTAX 15 indicates
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2.4. BASIC GL OPERATION 17 Display
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2.6. BEGIN/END PARADIGM 19 Table 2.
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2.6. BEGIN/END PARADIGM 21 Vertex C
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2.6. BEGIN/END PARADIGM 23 drawn us
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2.6. BEGIN/END PARADIGM 25 2 4 6 2
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2.6. BEGIN/END PARADIGM 27 Figure 2
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2.6. BEGIN/END PARADIGM 29 Primitiv
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2.7. VERTEX SPECIFICATION 31 to cha
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2.7. VERTEX SPECIFICATION 33 This c
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2.7. VERTEX SPECIFICATION 35 void C
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2.7. VERTEX SPECIFICATION 37 • si
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2.8. VERTEX ARRAYS 39 void VertexAt
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2.8. VERTEX ARRAYS 41 The index par
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2.8. VERTEX ARRAYS 43 void ArrayEle
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2.8. VERTEX ARRAYS 45 and Primitive
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2.8. VERTEX ARRAYS 47 not modified
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2.8. VERTEX ARRAYS 49 if (mode is i
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2.8. VERTEX ARRAYS 51 The command v
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2.8. VERTEX ARRAYS 53 if (no elemen
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2.8. VERTEX ARRAYS 55 format e t e
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2.9. BUFFER OBJECTS 57 Target name
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2.9. BUFFER OBJECTS 59 in the array
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2.9. BUFFER OBJECTS 61 If the GL is
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2.9. BUFFER OBJECTS 63 Name Value B
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2.9. BUFFER OBJECTS 65 Unmapping Bu
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2.9. BUFFER OBJECTS 67 binding corr
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2.11. RECTANGLES 69 void GenVertexA
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2.12. FIXED-FUNCTION VERTEX TRANSFO
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2.13. FIXED-FUNCTION VERTEX LIGHTIN
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2.14. VERTEX SHADERS 93 shader, its
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2.14. VERTEX SHADERS 95 If shader i
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2.14. VERTEX SHADERS 97 • One or
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2.14. VERTEX SHADERS 99 subsequent
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2.14. VERTEX SHADERS 101 Program pi
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2.14. VERTEX SHADERS 103 such a nam
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2.14. VERTEX SHADERS 105 • the in
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2.14. VERTEX SHADERS 107 LINK_STATU
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2.14. VERTEX SHADERS 109 Data type
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2.14. VERTEX SHADERS 111 This comma
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2.14. VERTEX SHADERS 113 the unifor
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2.14. VERTEX SHADERS 115 program is
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2.14. VERTEX SHADERS 117 control, t
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2.14. VERTEX SHADERS 119 active uni
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2.14. VERTEX SHADERS 121 Type Name
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2.14. VERTEX SHADERS 123 OpenGL Sha
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2.14. VERTEX SHADERS 125 For GetAct
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2.14. VERTEX SHADERS 127 The Unifor
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2.14. VERTEX SHADERS 129 void Progr
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2.14. VERTEX SHADERS 131 consecutiv
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2.14. VERTEX SHADERS 133 Uniform Bu
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2.14. VERTEX SHADERS 135 The number
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2.14. VERTEX SHADERS 137 subroutine
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2.14. VERTEX SHADERS 139 gram comma
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2.14. VERTEX SHADERS 141 recorded a
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2.14. VERTEX SHADERS 143 void GetTr
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2.14. VERTEX SHADERS 145 • If the
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2.14. VERTEX SHADERS 147 • the te
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2.14. VERTEX SHADERS 149 • The sa
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2.14. VERTEX SHADERS 151 The built-
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2.14. VERTEX SHADERS 153 results wr
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2.14. VERTEX SHADERS 155 a previous
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2.14. VERTEX SHADERS 157 • TEXTUR
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2.14. VERTEX SHADERS 159 • Data w
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2.15. TESSELLATION 161 • For each
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2.15. TESSELLATION 163 invocation m
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2.15. TESSELLATION 165 • The vari
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2.15. TESSELLATION 167 output varia
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2.15. TESSELLATION 169 Figure 2.13.
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2.15. TESSELLATION 171 Triangle Tes
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2.15. TESSELLATION 173 each triangl
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Page 229 and 230: 2.23. PRIMITIVE CLIPPING 209 gl_Bac
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Page 257 and 258: 3.6. POLYGONS 237 3.6.1 Basic Polyg
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Page 261 and 262: 3.6. POLYGONS 241 3.6.5 Depth Offse
Page 263 and 264: 3.7. PIXEL RECTANGLES 243 polygon r
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3.7. PIXEL RECTANGLES 281 B i and A
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¡ ¡ ¡ ¡ ¡ ¡ 3.8. BITMAPS 283
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3.10. TEXTURING 285 not be performe
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3.10. TEXTURING 287 The active text
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3.10. TEXTURING 289 FALSE is return
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3.10. TEXTURING 291 The currently b
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3.10. TEXTURING 293 The selected gr
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3.10. TEXTURING 295 might not suppo
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3.10. TEXTURING 297 exp p = max(−
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3.10. TEXTURING 299 Sized internal
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3.10. TEXTURING 301 Sized Base D S
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3.10. TEXTURING 303 When target is
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3.10. TEXTURING 305 TEXTURE_CUBE_MA
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3.10. TEXTURING 307 1.0 5.0 4 3 t v
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3.10. TEXTURING 309 Subsequent proc
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3.10. TEXTURING 311 components is c
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3.10. TEXTURING 313 result in an IN
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3.10. TEXTURING 315 storage modes c
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3.10. TEXTURING 317 • data points
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3.10. TEXTURING 319 FORMAT, and TEX
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3.10. TEXTURING 321 3.10.7 Buffer T
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3.10. TEXTURING 323 Internal format
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3.10. TEXTURING 325 Texture paramet
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3.10. TEXTURING 327 Major Axis Dire
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3.10. TEXTURING 329 bias texobj is
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3.10. TEXTURING 331 Coordinate Wrap
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3.10. TEXTURING 333 i 0 = wrap(⌊u
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3.10. TEXTURING 335 section 3.10.17
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3.10. TEXTURING 337 otherwise p =
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3.10. TEXTURING 339 level base arra
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3.10. TEXTURING 341 Effects of Samp
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3.10. TEXTURING 343 dimensional, re
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3.10. TEXTURING 345 for (i = 0; i <
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3.10. TEXTURING 347 } width = max(1
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3.10. TEXTURING 349 Texture Base Te
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3.10. TEXTURING 351 If the value of
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3.10. TEXTURING 353 SRCn_RGB OPERAN
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3.10. TEXTURING 355 Texture Compari
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3.10. TEXTURING 357 the second text
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3.10. TEXTURING 359 to image unit u
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3.10. TEXTURING 361 invalid if: •
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3.10. TEXTURING 363 Supported image
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3.10. TEXTURING 365 Texel sizes, co
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3.12. FOG 367 This factor f is comp
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3.13. FRAGMENT SHADERS 369 fragment
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3.13. FRAGMENT SHADERS 371 • Fog
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3.13. FRAGMENT SHADERS 373 version
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3.13. FRAGMENT SHADERS 375 defined
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3.13. FRAGMENT SHADERS 377 Such bin
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Chapter 4 Per-Fragment Operations a
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4.1. PER-FRAGMENT OPERATIONS 381 Fr
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4.1. PER-FRAGMENT OPERATIONS 383 st
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4.1. PER-FRAGMENT OPERATIONS 385 pr
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4.1. PER-FRAGMENT OPERATIONS 387 St
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4.1. PER-FRAGMENT OPERATIONS 389 Be
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4.1. PER-FRAGMENT OPERATIONS 391 dr
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4.1. PER-FRAGMENT OPERATIONS 393 vo
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4.1. PER-FRAGMENT OPERATIONS 395 Th
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4.1. PER-FRAGMENT OPERATIONS 397 to
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4.2. WHOLE FRAMEBUFFER OPERATIONS 3
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4.3. DRAWING, READING, AND COPYING
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4.4. FRAMEBUFFER OBJECTS 425 with t
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4.4. FRAMEBUFFER OBJECTS 427 If a f
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4.4. FRAMEBUFFER OBJECTS 429 BindRe
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4.4. FRAMEBUFFER OBJECTS 431 that t
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4.4. FRAMEBUFFER OBJECTS 433 or if
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4.4. FRAMEBUFFER OBJECTS 435 The re
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4.4. FRAMEBUFFER OBJECTS 437 • th
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4.4. FRAMEBUFFER OBJECTS 439 • An
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4.4. FRAMEBUFFER OBJECTS 441 of the
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4.4. FRAMEBUFFER OBJECTS 443 Effect
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4.4. FRAMEBUFFER OBJECTS 445 Conver
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Chapter 5 Special Functions This ch
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5.1. EVALUATORS 449 Integers Reals
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5.1. EVALUATORS 451 The second way
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5.2. SELECTION 453 EvalCoord2(p *
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5.3. FEEDBACK 455 of each primitive
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5.4. TIMER QUERIES 457 Type coordin
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5.5. DISPLAY LISTS 459 started or s
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5.5. DISPLAY LISTS 461 SHORT, UNSIG
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5.5. DISPLAY LISTS 463 Program and
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5.7. SYNC OBJECTS AND FENCES 465 Pr
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5.7. SYNC OBJECTS AND FENCES 467 vo
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5.8. HINTS 469 Target PERSPECTIVE_C
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6.1. QUERYING GL STATE 471 void Get
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6.1. QUERYING GL STATE 473 6.1.3 En
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6.1. QUERYING GL STATE 475 target m
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6.1. QUERYING GL STATE 477 • form
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6.1. QUERYING GL STATE 479 When the
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6.1. QUERYING GL STATE 481 format N
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6.1. QUERYING GL STATE 483 target m
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6.1. QUERYING GL STATE 485 resets a
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6.1. QUERYING GL STATE 487 names, a
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6.1. QUERYING GL STATE 489 If multi
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6.1. QUERYING GL STATE 491 To query
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6.1. QUERYING GL STATE 493 If pname
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6.1. QUERYING GL STATE 495 If pname
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6.1. QUERYING GL STATE 497 is a pro
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6.1. QUERYING GL STATE 499 command
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6.1. QUERYING GL STATE 501 void Get
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6.1. QUERYING GL STATE 503 • If p
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6.1. QUERYING GL STATE 505 An INVAL
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6.2. STATE TABLES 507 the attribute
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6.2. STATE TABLES 509 Type code Exp
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6.2. STATE TABLES 511 Get value Typ
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6.2. STATE TABLES 549 Get Command I
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6.2. STATE TABLES 565 Get Command M
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6.2. STATE TABLES 567 Get Command M
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Appendix A Invariance The OpenGL sp
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A.3. INVARIANCE RULES 581 • Sciss
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A.4. TESSELLATION INVARIANCE 583
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A.5. ATOMIC COUNTER INVARIANCE 585
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Appendix B Corollaries The followin
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589 16. ColorMaterial has no effect
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C.1. RGTC COMPRESSED TEXTURE IMAGE
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C.2. BPTC COMPRESSED TEXTURE IMAGE
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Appendix D Shared Objects and Multi
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D.2. SYNC OBJECTS AND MULTIPLE CONT
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D.3. PROPAGATING CHANGES TO OBJECTS
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E.1. CORE AND COMPATIBILITY PROFILE
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E.2. DEPRECATED AND REMOVED FEATURE
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E.2. DEPRECATED AND REMOVED FEATURE
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Appendix F Version 3.0 and Before O
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F.3. CHANGED TOKENS 619 New Token N
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F.5. CREDITS AND ACKNOWLEDGEMENTS 6
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F.5. CREDITS AND ACKNOWLEDGEMENTS 6
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G.2. DEPRECATION MODEL 625 state ha
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G.4. CREDITS AND ACKNOWLEDGEMENTS 6
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Appendix H Version 3.2 OpenGL versi
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H.4. CHANGE LOG 631 New Token Name
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H.5. CREDITS AND ACKNOWLEDGEMENTS 6
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H.5. CREDITS AND ACKNOWLEDGEMENTS 6
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I.2. DEPRECATION MODEL 637 ing fact
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I.4. CREDITS AND ACKNOWLEDGEMENTS 6
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J.1. NEW FEATURES 641 • Mechanism
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J.4. CREDITS AND ACKNOWLEDGEMENTS 6
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Appendix K Version 4.1 OpenGL versi
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K.5. CREDITS AND ACKNOWLEDGEMENTS 6
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Appendix L Version 4.2 OpenGL versi
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L.5. CREDITS AND ACKNOWLEDGEMENTS 6
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Appendix M Extension Registry, Head
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M.3. ARB EXTENSIONS 655 M.3.2 be am
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M.3. ARB EXTENSIONS 657 M.3.13 Text
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M.3. ARB EXTENSIONS 659 M.3.28 Open
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M.3. ARB EXTENSIONS 661 The name st
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M.3. ARB EXTENSIONS 663 equivalent
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M.3. ARB EXTENSIONS 665 M.3.59 Seam
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M.3. ARB EXTENSIONS 667 The name st
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M.3. ARB EXTENSIONS 669 M.3.84 Tess
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M.3. ARB EXTENSIONS 671 M.3.97 Cont
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M.3. ARB EXTENSIONS 673 M.3.109 Tex
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INDEX 675 552 ACTIVE UNIFORM BLOCKS
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INDEX 677 BindSampler, 290, 292 Bin
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INDEX 679 COLOR TABLE BIAS, 248, 24
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INDEX 681 CreateProgram, 96, 463 Cr
Page 703 and 704:
INDEX 683 DrawArraysInstanced, 48,
Page 705 and 706:
INDEX 685 Flush, 463, 464, 468, 587
Page 707 and 708:
INDEX 687 GetActiveAtomicCounterBuf
Page 709 and 710:
INDEX 689 GetVertexAttribdv, 498, 4
Page 711 and 712:
INDEX 691 GL ARB viewport array, 64
Page 713 and 714:
INDEX 693 IMAGE 2D RECT, 123 IMAGE
Page 715 and 716:
INDEX 695 512-514, 516, 518-525, 53
Page 717 and 718:
INDEX 697 MapGrid1, 451 MapGrid2, 4
Page 719 and 720:
INDEX 699 MAX SERVER WAIT TIMEOUT,
Page 721 and 722:
INDEX 701 MultTransposeMatrix, 72,
Page 723 and 724:
INDEX 703 POINT SIZE GRANULARITY, 5
Page 725 and 726:
INDEX 705 Q, 78, 79, 473 QUAD STRIP
Page 727 and 728:
INDEX 707 rgb10 a2ui, 362 RGB12, 29
Page 729 and 730:
INDEX 709 SecondaryColor3, 34 Secon
Page 731 and 732:
INDEX 711 TexCoord*1*, 33 TexCoord*
Page 733 and 734:
INDEX 713 526 TEXTURE CUBE MAP POS-
Page 735 and 736:
INDEX 715 triangles adjacency, 184
Page 737 and 738:
INDEX 717 417 UNSIGNED INT 8 8 8 8,
Page 739:
INDEX 719 VertexAttribI3i, 109 Vert
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