﻿ Geometric Tools: Corrections for GPGPU Programming for Games and Science

## Book Corrections for GPGPU Programming for Games and Science

 Book Corrections Organized by Date of Change 23 April 2015, page 337. Figure 6.10 has all the x-variables in upper case. They should be lower case. The paragraph before Equation (6.150) has a sentence starting with "For example,...". Revise this to "For example, suppose we rotate points about the up-axis in the Cartesian frame by a small angle θ. The top image of Figure 6.10 shows the action of the rotation in the x0 x1-plane for inputs (1,0,0) and (0,1,0). The bottom image of Figure 6.10 shows the same action, which is a rotation in the x'0 x'2-plane applied to the inputs (1,0,0) and (0,0,1)." 23 April 2015, page 340. The change of basis matrix C is on the wrong side of the terms. The equation V'i = CVi should be V'i = Σj Vj cij, where C = [cij]. The equation V' = CV should be V' = VC and the equation C = V'V-1 should be C = V-1V'. 7 November 2014, pages 24. Never say more than you have to. The sentence "Consequently, one-third is an irrational number base 2." should be deleted because it is incorrect. Rational numbers have either a finite number of bits or a repeating pattern of bits, so one-third is rational (consider 1/3 in base 10 that is 0.33...). The only conclusion desired here is that you cannot represent 1/3 as a binary scientific number using a finite number of bits. 7 November 2014, page 25. The sentence that contains equation (2.15) says "(1+α)/(1+β) ∈ (0,1)" but should say "(1+α)/(1+β) ∈ [1/2,1)". 7 November 2014, pages 26. The same issue occurs as on page 24. The phrase "when the rational number base 10 is irrational base 2" should say "when the rational number cannot be represented using a finite number of bits". 7 November 2014, pages 27. A simple spelling error. The last sentence of the first paragraph of Section 2.4.2 has "integers" that should be "integer". 7 November 2014, pages 361. Although equation (7.18) is syntactically correct, a reader suggested clarification to add parentheses around the summation: NT ( Σ n-1 i=0     Yi YiT) N 7 November 2014, pages 371. A simple grammar error. The caption for Figure 7.4 has "of a meshes" that should be "of meshes".
 Book Corrections Organized by Page Number Section 2.4, page 24. Never say more than you have to. The sentence "Consequently, one-third is an irrational number base 2." should be deleted because it is incorrect. Rational numbers have either a finite number of bits or a repeating pattern of bits, so one-third is rational (consider 1/3 in base 10 that is 0.33...). The only conclusion desired here is that you cannot represent 1/3 as a binary scientific number using a finite number of bits. Section 2.4.1 page 25. The sentence that contains equation (2.15) says "(1+α)/(1+β) ∈ (0,1)" but should say "(1+α)/(1+β) ∈ [1/2,1)". Section 2.4.1, pages 26. The same issue occurs as on page 24. The phrase "when the rational number base 10 is irrational base 2" should say "when the rational number cannot be represented using a finite number of bits". Section 2.4.2, pages 27. A simple spelling error. The last sentence of the first paragraph of Section 2.4.2 has "integers" that should be "integer". Section 6.4.4, page 337. Figure 6.10 has all the x-variables in upper case. They should be lower case. The paragraph before Equation (6.150) has a sentence starting with "For example,...". Revise this to "For example, suppose we rotate points about the up-axis in the Cartesian frame by a small angle θ. The top image of Figure 6.10 shows the action of the rotation in the x0 x1-plane for inputs (1,0,0) and (0,1,0). The bottom image of Figure 6.10 shows the same action, which is a rotation in the x'0 x'2-plane applied to the inputs (1,0,0) and (0,0,1)." Section 6.4.4, page 340. The change of basis matrix C is on the wrong side of the terms. The equation V'i = CVi should be V'i = Σj Vj cij, where C = [cij]. The equation V' = CV should be V' = VC and the equation C = V'V-1 should be C = V-1V'. Section 7.3.3.2, pages 361. Although equation (7.18) is syntactically correct, a reader suggested clarification to add parentheses around the summation: NT ( Σ n-1 i=0     Yi YiT) N Section 7.5, pages 371. A simple grammar error. The caption for Figure 7.4 has "of a meshes" that should be "of meshes".