Errata to _Graphics Gems II_, first edition, edited by Jim Arvo (arvo@cs.caltech.edu), Academic Press 1991. Code available online at http://www.graphicsgems.org/ compiled by Eric Haines (erich@acm.org) from author and reader contributions version 1.16 date: 9/10/08 ----- Errors in the text: p. xxix, middle of page: change "Rod G. Bogart (72)" to "Rod G. Bogart (72, 181)". p. 5, last line: change area of "7.5" to "5.5". (thanks to Nigel Stewart) p. 84, line 1: change "clockwise" to "counterclockwise". p. 85, line 1: change "counterclockwise" to "clockwise". p. 194, line 4: change "nil <- 0" to "int <- 0". p. 194, figure 3: change "a2.aF" to "e2.aF" and "a2.bF" to "e2.bF". p. 249, last sentence: change "less than 0, then" to "less than tnear, then". p. 323, first line: R2,1 is better as -R3,2. The reasoning: Given the 3x3 rotation matrix, R, as first stated on page 322, consider the case where cos(beta) == 0. Rather than reducing the matrix at this point, skip ahead to Thomas' next step and arbitrarily set gamma = 0. This gives us the knowledge that sin(gamma) == 0 and cos(gamma) == 1. Plugging these three facts into the matrix R, we arrive at the following matrix: 0 0 -sin(beta) sin(alpha)sin(beta) cos(alpha) 0 cos(alpha)sin(beta) -sin(alpha) 0 When sin(beta) == 1, it is acceptable to use R(2,1) and R(2,2) as Thomas indicates. However, when sin(beta) == -1, the result is not correct. The best choice seems to be to use -R(3,2) and R(2,2) to derive our value for alpha. The test case which prompted my investigation into this was a rotation described as euler XYZ angles (90,-90,0), which produces the following rotation matrix: 0 0 1 -1 0 0 0 -1 0 Using our code which was derived from the Graphics Gems II source, this produces a decomposed rotation value of (-90,-90,0) instead of the expected (90,-90,0). Under my modifications above, it reports the correct value. [Explanation from Joe Herdman] p. 340, Shear matrix: change "-(Q.v)w" to "-tan(phi)(Q.v)w". p. 420, line 10: "Berstein" should read "Bernstein". p. 448, flowchart: change the box with "D(r,j) > T?" to "D(r,j) < T?". [Thanks to Achim Mueller] p. 450, second line of equation set (3): the "floor" operator should be a ceiling operator, to match equation set (1). ----- The following are errors in the code listings (corrected in the online code at http://www.graphicsgems.org/). Note that many of the code listings online are different in minor and major ways from the code in the book (see Addenda, at the end, for new code not in the book). Serious errors (ones your compiler cannot or may not catch): p. 456: Delete FLOOR and CEILING macros (they're more like truncations). Change ROUND macro to (i.e. add parentheses around "a"): #define ROUND(a) ((a)>0 ? (int)((a)+0.5) : -(int)(0.5-(a))) Change SGN macro to (i.e. change positive condition result to "1"): #define SGN(a) (((a)<0) ? -1 : 1) p. 463, line 9: in V3Combine change last "result->y" to "result->z". p. 571, line 16: add missing macros: #define Trunc(v) ((int)floor(v)) /* normalize vector, return in pn */ #define unity(v,pn) { double len ; \ len = sqrt((v).x*(v).x+(v).y*(v).y+(v).z*(v).z) ; \ (pn)->x=(v).x/len; (pn)->y=(v).y/len; \ (pn)->z=(v).z/len; } p. 572, line 27: change "struct epthbuf_el {" to "struct depthbuf_el {" p. 574, 4th line from bottom: delete "break;" statement in order to move to next pair of edges p. 576, line 28: change "if ( t < 0.0 )" to "if ( t < tnear )" p. 591, line 7: change "*fp ==1.0;" to "*fp = 1.0;" p. 599, bottom: add lines: typedef struct { double x,y,z,w; } Vector4; Vector4 *V4MulPointByMatrix(); p. 600, line 6: add lines: #include #include "GraphicsGems.h" #include "unmatrix.h" p. 600, line 22: change to "Matrix4 pmat, invpmat, tinvpmat;" p. 600, line 25: change to "Point3 row[3], pdum3;" p. 600, line 29: change if ( pmat.element[3][3] != 0 ) to: if ( locmat.element[3][3] == 0 ) return 0; p. 600, line 39: change "pmat.element[4][3] = 1;" to "pmat.element[3][3] = 1;" p. 601, line 4: change: psol = *V4MulPointByMatrix(&prhs, &invpmat, &vdum4); to: Transpose( &invpmat, &tinvpmat ); V4MulPointByMatrix(&prhs, &tinvpmat, &psol); p. 602, line 5: change "&row[2])" to "&row[2], &pdum3)" p. 602, line 18: change "tran[U_ROTATEX] = atan2(row[1].x, row[1].y);" to "tran[U_ROTATEX] = atan2(-row[2].x, row[1].y);" [Thanks to Joe Herdman] p. 602, bottom: add the subroutines: /* transpose rotation portion of matrix a, return b */ Matrix4 *TransposeMatrix4(a, b) Matrix4 *a, *b; { int i, j; for (i=0; i<4; i++) for (j=0; j<4; j++) b->element[i][j] = a->element[j][i]; return(b); } /* multiply a hom. point by a matrix and return the transformed point */ Vector4 *V4MulPointByMatrix(pin, m, pout) Vector4 *pin, *pout; Matrix4 *m; { pout->x = (pin->x * m->element[0][0]) + (pin->y * m->element[1][0]) + (pin->z * m->element[2][0]) + (pin->w * m->element[3][0]); pout->y = (pin->x * m->element[0][1]) + (pin->y * m->element[1][1]) + (pin->z * m->element[2][1]) + (pin->w * m->element[3][1]); pout->z = (pin->x * m->element[0][2]) + (pin->y * m->element[1][2]) + (pin->z * m->element[2][2]) + (pin->w * m->element[3][2]); pout->w = (pin->x * m->element[0][3]) + (pin->y * m->element[1][3]) + (pin->z * m->element[2][3]) + (pin->w * m->element[3][3]); return(pout); } p. 604, line 7 from bottom: add code to check for singular matrix (near 0 determinant). Add code: /* Is the submatrix A singular? */ if ((det_1 == 0.0) || (ABS(det_1 / (pos - neg)) < PRECISION_LIMIT)) { /* Matrix M has no inverse */ fprintf (stderr, "affine_matrix4_inverse: singular matrix\n"); return FALSE; } ----- Syntax errors (ones your compiler or lint will catch): p. 458-466, throughout: replace "};" with "}" to make lint happy p. 464, gcd(): the variable "k" is set but not used - remove it p. 477, line 11 and p. 478, lines 15,18: change "coord" to "gcoord" and "last_coord" to "glast_coord" to avoid same name use for global and local variables p. 477, line 20: delete ", pos=0", since "pos" is not used in code. p. 483, v_convert code: change "alpha" to "alph", since "alpha" is a global defined in "types.h" p. 543, 547, 548: comment out text after "#else" and "#endif" statements (some compilers don't like this) p. 550, line 21: change "int i, num_iterations = 0;" to "int num_iterations = 0 ;", as "i" is not used p. 551, 2nd line from bottom: delete line "Matrix3 *vm;", as "vm" is not used p. 559, line 14: delete "int i;" declaration; "i" not used p. 573, line 15: delete "static" declaration from shadepoly p. 581 throughout: code is mostly for illustrative purposes; the RAY_REC, LIGHT_REC, TRIANGLE_REC, cache, object, and voxel structures need definition. Add lines: int i, hit ; float shadow_percent ; p. 588, 7th line from bottom: change "(j+0.5)" to "(dj+0.5)", or delete "dj = (double)j;" from previous line (dj currently is not used) 2nd line from bottom: change "(k+0.5)" to "(dk+0.5)", or delete "dk = (double)k;" from previous line (dk currently is not used) p. 594, middle: the "const" declarations before the TSpectra definitions create assignment incompatibilities; replace with "static". p. 596, first line of InitParams: change "int i, n=0;" to "int i;", since "n" is not used. p. 600, line 31: change "if ( det4x4(pmat) == 0.0 )" to "if ( det4x4(&pmat) == 0.0 )" (thanks to Joerg Scheurich, aka MUFTI, 9/10/2008) ----- The following are typographical errors in the comments: p. 461, line 19: change "transpose matrix a," to "transpose rotation portion of matrix a," p. 473, line 28: change "condititions:" to "conditions:" p. 514, line 2: change "clockwise" to "counterclockwise" p. 576, line 30: change "hit near face," to "hit far face," p. 578, line 21: change "coefficents" to "coefficients" p. 584, line 12: change "nubmer" to "number" p. 588, line 5: change "arrary" to "array" p. 590, line 10: change "radom" to "random" p. 595, line 24: change "quarilateral" to "quadrilateral" p. 610, line 2: change "varients" to "variants" ----- Addenda: Not include in the gem "Intersecting a Ray with an Elliptical Torus" is the following code which compensates for the order of the roots being transposed. It was not included since it would make the gem dependent on the behaviour of the root solver. Insert after the call to SolveQuartic (middle of p. 579): /* SolveQuartic returns root pairs in reversed order. */ if ( *nhits > 1 ) m = rhits[0]; u = rhits[1]; rhits[0] = u; rhits[1] = m; if ( *nhits > 3 ) m = rhits[2]; u = rhits[3]; rhits[2] = u; rhits[3] = m; Also, note that the torus intersector may not handle degenerate surfaces (e.g. where the major radius < minor radius, or major radius < 0) as desired. Xiaolin Wu's code for "Efficient Statistical Computations for Optimal Color Quantization" is available online in quantizer.c, though not in the book. The code originally distributed has been modified slightly, with the global variable "m2" renamed to "gm2" to avoid confusion with the local "m2" in some routines. The Var() function has had a fix to it, the absolute value of the result is now returned. Code for Greg Ward's "Real Pixels" article is not in the book, but is included in the RealPixels subdirectory of the online code. The code provided in the online distribution for Greg Ward's "A Recursive Implementation of the Perlin Noise Function" (noise3.c) has a variety of functions available (e.g. fractal noise), more than the code in the text. Included in the distribution code is c_format, a PostScript typesetting program for C source code (v0.6) by Dale Schumacher. There is a tester provided for Alan Paeth and David Schilling's "Of Integers, Fields, and Bit Counting".