Differential D15540 Diff 43017 libs/flake/KoPathSegment.cpp

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libs/flake/KoPathSegment.cpp

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820 our chord line is of the form: 820​ our chord line is of the form:
821 (2) ax + by + c = 0 821​ (2) ax + by + c = 0
822 we can determine the distance d(t) from any point P(t) to our chord 822​ we can determine the distance d(t) from any point P(t) to our chord
823 by substituting formula (1) into formula (2): 823​ by substituting formula (1) into formula (2):
824 d(t) = sum_i d_i B_{n,i}(t), where d_i = a*x_i + b*y_i + c 824​ d(t) = sum_i d_i B_{n,i}(t), where d_i = a*x_i + b*y_i + c
825 which forms another explicit bezier curve 825​ which forms another explicit bezier curve
826 D(t) = (t,d(t)) = sum_i D_i B_{n,i}(t) 826​ D(t) = (t,d(t)) = sum_i D_i B_{n,i}(t)
827 now values of t for which P(t) lies outside of our fat line L 827​ now values of t for which P(t) lies outside of our fat line L
828 corrsponds to values of t for which D(t) lies above d = dmax or 828​ corresponds to values of t for which D(t) lies above d = dmax or
829 below d = dmin 829​ below d = dmin
830 we can determine parameter ranges of t for which P(t) is guaranteed 830​ we can determine parameter ranges of t for which P(t) is guaranteed
831 to lie outside of L by identifying ranges of t which the convex hull 831​ to lie outside of L by identifying ranges of t which the convex hull
832 of D(t) lies above dmax or below dmin 832​ of D(t) lies above dmax or below dmin
833 */ 833​ */
834 // now calculate the control points of D(t) by using the signed 834​ // now calculate the control points of D(t) by using the signed
835 // distances of P_i to our chord 835​ // distances of P_i to our chord
836 KoPathSegment dt; 836​ KoPathSegment dt;
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