C 代码 返回任何多项式积分的精确值 在 2D 中任意三角形的内部.rar

21 January 2020 11:07:20 AM TRIANGLE_INTEGRALS_TEST: C version. Test the TRIANGLE_INTEGRALS library. I4_TO_PASCAL_TEST I4_TO_PASCAL converts a linear index to Pascal triangle indices. K => I J 1 0 0 2 1 0 3 0 1 4 2 0 5 1 1 6 0 2 7 3 0 8 2 1 9 1 2 10 0 3 11 4 0 12 3 1 13 2 2 14 1 3 15 0 4 16 5 0 17 4 1 18 3 2 19 2 3 20 1 4 I4_TO_PASCAL_DEGREE_TEST I4_TO_PASCAL_DEGREE converts a linear index to the degree of the corresponding Pascal triangle indices. K => D 1 0 2 1 3 1 4 2 5 2 6 2 7 3 8 3 9 3 10 3 11 4 12 4 13 4 14 4 15 4 16 5 17 5 18 5 19 5 20 5 PASCAL_TO_I4_TEST PASCAL_TO_I4 converts Pascal triangle indices to a linear index. I J => K 0 0 1 1 0 2 0 1 3 2 0 4 1 1 5 0 2 6 3 0 7 2 1 8 1 2 9 0 3 10 4 0 11 3 1 12 2 2 13 1 3 14 0 4 15 R8MAT_PRINT_TEST R8MAT_PRINT prints an R8MAT. The matrix: Col: 0 1 2 3 Row 0: 11 12 13 14 1: 21 22 23 24 2: 31 32 33 34 3: 41 42 43 44 4: 51 52 53 54 5: 61 62 63 64 R8MAT_PRINT_SOME_TEST R8MAT_PRINT_SOME prints some of an R8MAT. Rows 2:4, Cols 1:2: Col: 0 1 Row 1: 21 22 2: 31 32 3: 41 42 TRINOMIAL_TEST TRINOMIAL evaluates the trinomial coefficient: T(I,J,K) = (I+J+K)! / I! / J! / K! I J K T(I,J,K) 0 0 0 1 1 0 0 1 2 0 0 1 3 0 0 1 4 0 0 1 0 1 0 1 1 1 0 2 2 1 0 3 3 1 0 4 4 1 0 5 0 2 0 1 1 2 0 3 2 2 0 6 3 2 0 10 4 2 0 15 0 3 0 1 1 3 0 4 2 3 0 10 3 3 0 20 4 3 0 35 0 4 0 1 1 4 0 5 2 4 0 15 3 4 0 35 4 4 0 70 0 0 1 1 1 0 1 2 2 0 1 3 3 0 1 4 4 0 1 5 0 1 1 2 1 1 1 6 2 1 1 12 3 1 1 20 4 1 1 30 0 2 1 3 1 2 1 12 2 2 1 30 3 2 1 60 4 2 1 105 0 3 1 4 1 3 1 20 2 3 1 60 3 3 1 140 4 3 1 280 0 4 1 5 1 4 1 30 2 4 1 105 3 4 1 280 4 4 1 630 0 0 2 1 1 0 2 3 2 0 2 6 3 0 2 10 4 0 2 15 0 1 2 3 1 1 2 12 2 1 2 30 3 1 2 60 4 1 2 105 0 2 2 6 1 2 2 30 2 2 2 90 3 2 2 210 4 2 2 420 0 3 2 10 1 3 2 60 2 3 2 210 3 3 2 560 4 3 2 1260 0 4 2 15 1 4 2 105 2 4 2 420 3 4 2 1260 4 4 2 3150 0 0 3 1 1 0 3 4 2 0 3 10 3 0 3 20 4 0 3 35 0 1 3 4 1 1 3 20 2 1 3 60 3 1 3 140 4 1 3 280 0 2 3 10 1 2 3 60 2 2 3 210 3 2 3 560 4 2 3 1260 0 3 3 20 1 3 3 140 2 3 3 560 3 3 3 1680 4 3 3 4200 0 4 3 35 1 4 3 280 2 4 3 1260 3 4 3 4200 4 4 3 11550 0 0 4 1 1 0 4 5 2 0 4 15 3 0 4 35 4 0 4 70 0 1 4 5 1 1 4 30 2 1 4 105 3 1 4 280 4 1 4 630 0 2 4 15 1 2 4 105 2 2 4 420 3 2 4 1260 4 2 4 3150 0 3 4 35 1 3 4 280 2 3 4 1260 3 3 4 4200 4 3 4 11550 0 4 4 70 1 4 4 630 2 4 4 3150 3 4 4 11550 4 4 4 34650 RS_TO_XY_MAP_TEST: RS_TO_XY_MAP determines the coefficients of the linear map from a the reference in RS coordinates to the physical triangle in XY coordinates: X = a + b * R + c * S Y = d + e * R + f * S XY triangle vertices: Col: 0 1 2 Row 0: 2 3 0 1: 0 4 3 Mapping coefficients are: X = 2 + 1 * R + -2 * S Y = 0 + 4 * R + 3 * S Apply map to RS triangle vertices. Recover XY vertices (2,0), (3,4) and (0,3). V(0) = ( 2,0) V(1) = ( 3,4) V(2) = ( 0,3) XY_TO_RS_MAP_TEST: XY_TO_RS_MAP determines the coefficients of the linear map from a general triangle in XY coordinates to the reference triangle in RS coordinates: R = a + b * X + c * Y S = d + e * X + f * Y XY triangle vertices: Col: 0 1 2 Row 0: 2 3 0 1: 0 4 3 Mapping coefficients are: R = -0.545455 + 0.272727 * X + 0.181818 * Y S = 0.727273 + -0.363636 * X + 0.0909091 * Y Apply map to XY triangle vertices. Recover RS vertices (0,0), (1,0) and (0,1). V[0] = (0,0) V[1] = (1,1.11022e-16) V[2] = (0,1) POLY_PRINT_TEST: POLY_PRINT can print a D-degree polynomial in X and Y. P1(x,y) = 12.34 p1(x,y) = +12.34 P2(x,y) = 1 + 2 * x + 3 * Y p2(x,y) = +1 +2 x +3 y P3(x,y) = xy p3(x,y) = xy = 0 P4(x,y) = 1.0 - 2.1 * x + 3.2 * y - 4.3 * x^2 + 5.4 * xy - 6.5 * y^2 + 7.6 * x^3 - 8.7 * x^2y + 9.8 * xy^2 - 10.9 * y^3. p4(x,y) = +1 -2.1 x +3.2 y -4.3 x^2 +5.4 xy -6.5 y^2 +7.6 x^3 -8.7 x^2y +9.8 xy^2 -10.9 y^3 POLY_POWER_LINEAR_TEST: POLY_POWER_LINEAR computes the N-th power of a linear polynomial in X and Y. p1(x,y)