0b491a01-581d-44dd-b0b3-b6300c065474 12 ioan92 4 5 false false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Dr Ioan DIACU

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HYPERBOLIC PARABOLOID - GEOMETRICAL CARACTERISTICS

Based on:

https://les-mathematiques.net/vanilla/discussion/1802966/volume-hexaedre-et-pentaedre-quelconques#latest

XYZ ParabHyperb all MaximaTakeover X XYZ 1 col : Y XYZ 2 col : Z XYZ 3 col : 13 mat x0 y0 z0 x1 y1 z1 x2 y2 z2 x3 y3 z3 43 mat XYZ : U 1 s - (1 t - (* s 1 t - (* s t * 1 s - (t * 41 mat : s t f X U * : s t g Y U * : s t h Z U * : 31 mat 13 mat s t J s t f s diff s t f t diff s t g s diff s t g t diff 22 mat det Maxima : Vol s t h s t J * (s 01 int t 01 int Maxima : S.x s t f s t h * s t J * (s 01 int t 01 int Maxima : S.y s t g s t h * s t J * (s 01 int t 01 int Maxima : I.xG0 s t f (2^s t h * s t J * (s 01 int t 01 int Maxima : I.yG0 s t g (2^s t h * s t J * (s 01 int t 01 int Maxima : I.xyG0 s t f s t g * s t h * s t J * (s 01 int t 01 int Maxima : x.G y.G 12 mat S.x S.y 12 mat Vol / : I.xG I.yG I.xyG 13 mat I.xG0 I.yG0 I.xyG0 13 mat Vol y.G 2^x.G 2^x.G y.G * 13 mat * - : Vol x.G y.G 031 mat I.xG0 I.yG0 I.xyG0 31 mat I.xG I.yG I.xyG 31 mat 14 mat 131 line :

XYZ 3452 - 415 - 5 - 624 - 243 mat :

XYZ 0020121 - 121 - 0243 mat :

RPH XYZ ParabHyperb :

SYMBOLIC OPTIMISATION - WRONG RESULTS Vol x.G y.G xx 31 mat I.xG0 I.yG0 I.xyG0 31 mat I.xG I.yG I.xyG 31 mat 14 mat RPH : 2 0.0833 - 0.0833 - 0.1667 - 0.1667 - 41 mat 0.0833 0.1667 0.1667 0.0833 41 mat 031 mat 0.0833 0.0833 0.25 0.25 41 mat 0.0833 0.25 0.25 0.0833 41 mat 0.0556 - 0.1111 - 0.2222 - 0.1111 - 41 mat 31 mat 0.0556 - 0.0556 - 0.1111 0.1111 41 mat 0.0556 - 0.1111 0.1111 0.0556 - 41 mat 0.0694 0.0139 0.0972 - 0.0139 41 mat 31 mat 14 mat

x0 y0 z0 x1 y1 z1 x2 y2 z2 x3 y3 z3 43 mat Vol x.G y.G 031 mat I.xG0 I.yG0 I.xyG0 31 mat I.xG I.yG I.xyG 31 mat 14 mat Clear 1

Separate Symbolical Developement and Numerical Application Use - Good Results !!! but too long "saussages" : XYZ RGeoPH x0 y0 z0 x1 y1 z1 x2 y2 z2 x3 y3 z3 43 mat XYZ : Vol 2 x2 x0 - (* y3 * x1 x0 + 2 x3 * - (y2 * + x0 x2 - (y1 * + x2 x1 + 2 x3 * - (y0 * - (z3 * x1 x0 + 2 x2 * - (y3 * - 2 x1 x3 - (* y2 * + x3 x0 + 2 x2 * - (y1 * + x3 x1 - (y0 * + (z2 * + x2 x0 - (y3 * x3 x0 + 2 x1 * - (y2 * - 2 x0 x2 - (* y1 * + x3 x2 + 2 x1 * - (y0 * + (z1 * + x2 x1 + 2 x0 * - (y3 * x1 x3 - (y2 * + x3 x2 + 2 x0 * - (y1 * - 2 x3 x1 - (* y0 * + (z0 * + 12 / : xG 3 x2 x0 - (* x2 x0 + 2 x3 * + (* y3 * x1 3 x2 2 x3 * + (* - 2 x0 * + (x3 * x0 2 x1 * + (x2 * + x1 x1 x0 + (* + x0 2^+ (y2 * + x0 x2 - (x3 * x2 x1 2 x2 * + (* - x0 x1 2 x0 * + (* + (y1 * + x1 2 x2 3 x3 * - (* + 3 x0 * - (x3 * x2 x2 x1 + x0 + (* + x1 x1 2 x0 * + (* + (y0 * - (z3 * x1 3 x2 * - 2 x0 * + (x3 * x0 2 x1 3 x2 * - (* + (x2 * + x1 x1 x0 + (* + x0 2^+ (y3 * - 3 x3 x3 2 x2 * + (* - x1 x1 2 x2 * + (* + (* y2 * + x3 x3 x1 + x0 + 2 x2 * + (* x2 x0 - 3 x1 2 x2 * + (* + (* - x0 x0 2 x1 * + (* + (y1 * + x3 x2 x0 + 2 x3 * + (* x1 x2 x0 + 2 x1 * + (* - (y0 * + (z2 * + x2 x0 - (x3 * x2 x1 2 x2 * + (* + x0 x1 2 x0 * + (* - (y3 * x3 x3 x1 + x0 + 2 x2 * + (* x0 - 3 x1 * + (x2 2 x1 * + (* - x0 2^+ (y2 * - 3 x2 x2 2 x1 * + (* - x0 x0 2 x1 * + (* + (* y1 * + x3 x3 x2 + x1 + 2 x0 * + (* x2 x2 x0 + 2 x1 * + (* + 3 x1 * x0 2 x1 * + (* - (y0 * + (z1 * + x1 2 x2 * + 3 x0 * - (x3 * x2 x2 x1 + x0 + (* + x1 x1 2 x0 * + (* + 6 x0 2^* - (y3 * x1 x2 x0 + 2 x1 * + (* x3 x2 x0 + 2 x3 * + (* - (y2 * + x3 x3 x2 + x1 + 2 x0 * + (* x2 x2 x0 + 2 x1 * + (* + 3 x0 * x1 2 x0 * + (* - (y1 * - 3 x3 x3 2 x0 * + (* - x1 x1 2 x0 * + (* + (* y0 * - (z0 * + 62 x2 x0 - (* y3 * x1 x0 + 2 x3 * - (y2 * + x0 x2 - (y1 * + x2 x1 + 2 x3 * - (y0 * - (z3 * x1 x0 + 2 x2 * - (y3 * - 2 x1 x3 - (* y2 * + x3 x0 + 2 x2 * - (y1 * + x3 x1 - (y0 * + (z2 * + x2 x0 - (y3 * x3 x0 + 2 x1 * - (y2 * - 2 x0 x2 - (* y1 * + x3 x2 + 2 x1 * - (y0 * + (z1 * + x2 x1 + 2 x0 * - (y3 * x1 x3 - (y2 * + x3 x2 + 2 x0 * - (y1 * - 2 x3 x1 - (* y0 * + (z0 * + (* / : yG y3 6 x2 x0 - (* y3 * x1 3 x2 2 x3 * - (* + 2 x0 * + (y2 * + x0 x2 - (y1 * + x1 2 x2 - 3 x3 * + (* - 3 x0 * + (y0 * - (* y2 x0 3 x3 * - 2 x1 * + (y2 * x1 x0 + 2 x2 * - (y1 * + x0 x2 - (y0 * + (* + y1 x0 x2 - (y1 * x2 x1 + 2 x0 * - (y0 * - (* + x2 3 x3 * - 2 x1 * + (y0 2^* - (z3 * y3 x1 3 x2 * - 2 x0 * + (y3 * x0 3 x3 - 2 x2 * + (* - 2 x1 * + (y2 * + x3 x1 - (y1 * - x1 x0 + 2 x3 * - (y0 * + (* - y2 6 x1 x3 - (* y2 * x0 2 x3 3 x2 * - (* + 3 x1 * + (y1 * + x3 x1 - (y0 * + (* + y1 x3 3 x2 * - 2 x0 * + (y1 * x3 x0 + 2 x1 * - (y0 * + (* + x3 x1 - (y0 2^* + (z2 * + y3 x2 x0 - (y3 y1 + (* x3 x0 + 2 x2 * - (y2 * - x3 x2 + 2 x0 * - (y0 * + (* y2 x0 2 x3 * + 3 x1 * - (y2 * x3 3 x2 - 2 x1 * + (* - 2 x0 * + (y1 * + x2 x0 - (y0 * - (* - y1 6 x0 x2 - (* y1 * x3 2 x2 3 x1 * - (* + 3 x0 * + (y0 * + (* + x2 2 x3 * + 3 x1 * - (y0 2^* + (z1 * + y3 x1 2 x2 * + 3 x0 * - (y3 * x2 x1 + 2 x3 * - (y2 * + x1 x3 - (y1 * + x2 3 x3 2 x0 * - (* + 2 x1 * + (y0 * + (* y2 x1 x3 - (y2 y0 + (* x3 x2 + 2 x1 * - (y1 * - (* + y1 x3 2 x2 * + 3 x0 * - (y1 * x2 2 x3 - 3 x0 * + (* - 3 x1 * + (y0 * + (* - 6 x3 x1 - (* y0 2^* + (z0 * + 62 x2 x0 - (* y3 * x1 x0 + 2 x3 * - (y2 * + x0 x2 - (y1 * + x2 x1 + 2 x3 * - (y0 * - (z3 * x1 x0 + 2 x2 * - (y3 * - 2 x1 x3 - (* y2 * + x3 x0 + 2 x2 * - (y1 * + x3 x1 - (y0 * + (z2 * + x2 x0 - (y3 * x3 x0 + 2 x1 * - (y2 * - 2 x0 x2 - (* y1 * + x3 x2 + 2 x1 * - (y0 * + (z1 * + x2 x1 + 2 x0 * - (y3 * x1 x3 - (y2 * + x3 x2 + 2 x0 * - (y1 * - 2 x3 x1 - (* y0 * + (z0 * + (* / : IxG0 12 x2 x0 - (* x2 x2 x0 + (* x0 2^+ x3 3 x3 * 2 x2 x0 + (* + (* + (* y3 * x3 3 x3 * x1 43 x3 * 2 x2 * + (* - 3 x0 * + (* 23 x1 x0 + 2 x2 * - (x2 * x0 2^+ (* x1 x1 2 x0 * + (* + (* + (* x2 3 x0 3 x1 * + (* x2 * 2 x1 3 x1 * 2 x0 * + (* x0 2^+ (* + (* + 3 x1 x1 x1 x0 + (* x0 2^+ (* x0 3^+ (* + (y2 * + x3 3 x0 x2 - (* x3 * 2 x0 x1 3 x0 * + (* x2 x1 3 x2 * + (* - (* + (* x2 x2 x0 33 x2 * 2 x1 * + (* + (* 3 x1 2^* + x0 2^- (* - 3 x0 * x1 x1 2 x0 * + (* 3 x0 2^* + (* + (y1 * + x3 3 x1 3 x2 4 x3 * - (* + 8 x0 * - (* x3 * 2 x2 3 x2 x0 + (* 2 x1 * + (* x1 x1 3 x0 * + (* + 6 x0 2^* - (* + (* x2 x2 3 x2 x1 + (* 2 x0 * + (* x1 3 x1 * 4 x0 * + (* + 3 x0 2^* + (* + 3 x1 * x1 x1 2 x0 * + (* 3 x0 2^* + (* + (y0 * - (z3 * x3 3 x1 4 x2 * - 3 x0 * + (* x3 * 23 x1 x0 + 4 x2 * - (x2 * x0 2^+ (* x1 x1 2 x0 * + (* + (* + (* x2 3 x0 3 x1 4 x2 * - (* + (* x2 * 2 x1 3 x1 * 2 x0 * + (* x0 2^+ (* + (* + 3 x1 x1 x1 x0 + (* x0 2^+ (* x0 3^+ (* + (y3 * - 12 x3 x3 x3 2 x2 * + (* 3 x2 2^* + (* - x1 x2 3 x2 * 2 x1 * + (* x1 2^+ (* + (* y2 * + x3 x3 3 x3 x0 + (* 2 x1 3 x2 * + (* + (* x2 9 x2 * 23 x1 * 2 x0 * + (* + (* + x1 3 x1 * 4 x0 * + (* + 3 x0 2^* + (* x2 23 x0 2 x1 * - (* x1 * x0 2^+ (* 3 x2 * x0 - 43 x2 * 2 x1 * + (* + (* - (* + 3 x0 * x1 3 x1 * 2 x0 * + (* x0 2^+ (* + (y1 * + x3 x3 x1 33 x3 * 2 x2 x0 + (* + (* + (* x2 3 x2 * 2 x0 * + (* + x1 2^- 3 x0 2^* + (* x1 x2 3 x2 * 2 x0 3 x1 * + (* + (* 3 x1 3 x1 * 2 x0 * + (* x0 2^+ (* + (* - (y0 * + (z2 * + x3 3 x2 x0 - (* x3 * 2 x0 x1 3 x0 * + (* x2 x1 3 x2 * + (* - (* - (* x2 x2 x0 33 x2 * 2 x1 * + (* + (* 3 x1 2^* + x0 2^- (* + 3 x0 * x1 x1 2 x0 * + (* 3 x0 2^* + (* - (y3 * x3 x3 3 x3 x0 + (* 2 x1 3 x2 * + (* + (* x2 9 x2 * 23 x1 * 2 x0 * + (* + (* + x1 3 x1 * 4 x0 * + (* + 3 x0 2^* + (* - x2 3 x0 - 4 x1 * + (* x2 * 23 x1 * x0 - 4 x1 * + (* x0 2^- (* + (* + 3 x1 3 x1 * x0 - 4 x1 * + (* 2 x0 2^* - (* x0 3^- (* + (y2 * + 12 x2 x2 x2 2 x1 * + (* 3 x1 2^* + (* - x0 x1 3 x1 * 2 x0 * + (* x0 2^+ (* + (* y1 * + x3 x3 3 x3 x2 + 2 x0 * + (* 2 x1 * + (* x2 3 x2 * 4 x1 x0 + (* + (* + 3 x1 x1 2 x0 * + (* 3 x0 2^* + (* + (* x2 x2 3 x2 * 2 x0 3 x1 * + (* + (* 3 x1 3 x1 * 2 x0 * + (* x0 2^+ (* + (* + 12 x1 * x1 3 x1 * 2 x0 * + (* x0 2^+ (* - (y0 * + (z1 * + x3 3 x1 3 x2 * + 4 x0 * - (* x3 * 2 x2 3 x2 x0 + (* 2 x1 * + (* x1 x1 3 x0 * + (* + 12 x0 2^* - (* + (* x2 x2 3 x2 x1 + (* 2 x0 * + (* x1 3 x1 * 4 x0 * + (* + 3 x0 2^* + (* + 3 x1 x1 x1 2 x0 * + (* 3 x0 2^* + (* 12 x0 3^* - (* + (y3 * x1 x2 3 x2 * 2 x0 3 x1 * + (* + (* 3 x1 3 x1 * 2 x0 * + (* x0 2^+ (* + (* x3 x3 x1 33 x3 * 2 x2 x0 + (* + (* + (* x2 3 x2 * 2 x0 * + (* + x1 2^- 3 x0 2^* + (* - (y2 * + x3 x3 3 x3 x2 + 2 x0 * + (* 2 x1 * + (* x2 3 x2 * 4 x1 x0 + (* + (* + 3 x1 x1 2 x0 * + (* 3 x0 2^* + (* + (* x2 x2 3 x2 * 2 x0 3 x1 * + (* + (* 3 x1 3 x1 * 2 x0 * + (* x0 2^+ (* + (* + 12 x0 * x1 x1 2 x0 * + (* 3 x0 2^* + (* - (y1 * - 12 x3 x3 x3 2 x0 * + (* 3 x0 2^* + (* - x1 x1 x1 2 x0 * + (* 3 x0 2^* + (* + (* y0 * - (z0 * + 720 / : IyG0 y3 3 y3 * 12 x2 x0 - (* y3 * x1 42 x2 * 3 x3 * - (* + 3 x0 * + (y2 * + x0 x2 - (y1 * + x1 3 x2 - 4 x3 * + (* - 8 x0 * + (y0 * - (* 2 y2 3 x1 x0 + 2 x2 2 x3 * - (* + (y2 * x0 x2 - (y0 * + (* x1 3 x2 * - 2 x0 * + (y1 * + (* y1 x0 x2 - (y1 * x1 2 x2 * + 3 x0 * - (y0 * - (* + 3 x2 x1 + 2 x0 2 x3 * - (* + (* y0 2^* - (* + (* y2 y2 3 x0 4 x3 * - 3 x1 * + (y2 * x0 3 x2 * - 2 x1 * + (y1 * + (* x1 3 x2 * - 2 x0 * + (y0 * + (* y1 3 x1 x0 + 2 x2 * - (* y1 * 4 x0 x2 - (* y0 * + (* + x1 2 x2 * + 3 x0 * - (y0 2^* - (* + 3 y1 y1 x0 x2 - (y1 * x2 x1 + 2 x0 * - (y0 * - (* x2 2 x1 * + 3 x0 * - (y0 2^* - (* x2 4 x3 * - 3 x1 * + (y0 3^* - (* + (z3 * y3 y3 3 x1 4 x2 * - 3 x0 * + (y3 * 2 x1 x0 + 2 x3 - 2 x2 * + (* - (* y2 * + x1 3 x3 * - 2 x0 * + (y0 * + (* x0 3 x3 * - 2 x1 * + (y1 * + (* - y2 23 x3 x1 - (* y1 * x0 3 x3 * - 2 x1 * + (y0 * - (* 3 x0 43 x2 * 2 x3 * - (* - 3 x1 * + (* y2 * - (* + y1 x0 2 x3 * + 3 x1 * - (y1 * 4 x3 x1 - (* y0 * + (* + 3 x1 x0 + 2 x3 * - (* y0 2^* - (* y2 3 y2 * 12 x1 x3 - (* y2 * x0 3 x3 4 x2 * - (* + 8 x1 * + (y1 * + x3 x1 - (y0 * + (* 2 y1 3 x3 x0 + 2 x1 2 x2 * - (* + (* y1 * x0 2 x3 * + 3 x1 * - (y0 * + (* x3 x1 - (y0 2^* + (* + (* + 3 y1 y1 x3 4 x2 * - 3 x0 * + (y1 * x3 3 x1 * - 2 x0 * + (y0 * + (* x3 x0 + 2 x1 * - (y0 2^* + (* x3 x1 - (y0 3^* + (* + (z2 * + y3 y3 3 x2 x0 - (y3 * x3 x0 + 2 x2 * - (y2 * - x3 x2 + 2 x0 * - (y0 * + (* 2 x2 x0 - (* y1 * + (* y2 2 x3 3 x2 * - 2 x0 * + (y1 * - 2 x2 x0 - (* y0 * + (* 3 x0 2 x3 * + 3 x2 * - (* y2 * - (* + y1 3 x2 x0 - (* y1 * 2 x3 2 x2 * + 3 x0 * - (* y0 * + (* + 3 x2 2 x3 * + 3 x0 * - (* y0 2^* + (* y2 y2 3 x0 3 x3 * + 4 x1 * - (y2 * 2 x3 x0 + 2 x2 2 x1 * - (* + (* y1 * + (* x3 3 x2 * - 2 x0 * + (y0 * + (* - 3 y1 * x3 42 x2 * 3 x1 * - (* + 3 x0 * + (y1 * - 2 x2 x0 - (* y0 * + (* + x3 2 x2 * + 3 x0 * - (y0 2^* + (* + 3 y1 y1 12 x0 x2 - (* y1 * x3 3 x2 4 x1 * - (* + 8 x0 * + (y0 * + (* 2 x3 x2 + 2 x0 2 x1 * - (* + (* y0 2^* + (* x2 3 x3 * + 4 x1 * - (y0 3^* + (* + (z1 * + y3 y3 3 x1 3 x2 * + 4 x0 * - (y3 * x1 3 x3 * - 2 x2 * + (y2 * + 2 x2 x1 + 2 x3 2 x0 * - (* + (* y0 * + (* x2 3 x3 * - 2 x1 * + (y1 * + (* y2 3 x2 x1 + 2 x3 * - (* y2 * 22 x1 x3 - (* y1 * x2 3 x3 * - 2 x1 * + (y0 * + (* + (* + y1 x2 2 x3 * + 3 x1 * - (y1 * - 6 x1 x3 - (* y0 * + (* + 3 x2 42 x3 * 3 x0 * - (* + 3 x1 * + (* y0 2^* + (* y2 y2 3 x1 x3 - (y2 * x3 x2 + 2 x1 * - (y1 * - (* 2 x1 x3 - (* y0 * + (* y1 3 x3 2 x2 * + 3 x1 * - (* y1 * 2 x2 2 x3 * + 3 x1 * - (* y0 * + (* - 3 x1 x3 - (* y0 2^* + (* + 312 x3 x1 - (* y0 3^* y1 y1 x3 3 x2 * + 4 x0 * - (y1 * 2 x3 x2 + 2 x1 2 x0 * - (* + (* y0 * + (* x2 3 x3 4 x0 * - (* + 8 x1 * + (y0 2^* + (* - (* + (z0 * + 720 / : IxyG0 y3 12 x2 x0 - (* x2 x0 + 3 x3 * + (* y3 * 3 x1 3 x0 4 x3 * - (* + (x3 * x2 x1 x0 + 4 x2 * + (* + x0 2^+ (* x1 x1 2 x0 * + (* + (y2 * + x0 x2 - (x1 3 x3 x2 + x0 + (* + (* y1 * + 3 x1 3 x2 4 x3 * - (* + (x3 * x2 2^+ x0 x1 4 x0 * + (* + (* 2 x1 * 3 x0 * + (x2 * + x1 2^+ (y0 * - (* y2 3 x3 x1 x0 + 4 x3 x2 + (* - (* x0 3 x1 * + (x2 * + x1 2^+ (* x0 x0 2 x1 * + (* + (y2 * x1 3 x2 * - 2 x0 * + (x3 * x0 9 x2 * - (x2 * + 3 x1 * x1 x0 + (* + 2 x0 2^* + (y1 * + x0 x2 - (x1 3 x3 x2 + x0 + (* + (* y0 * + (* + y1 x0 x2 - (x3 * 3 x0 x1 x0 + (* x2 x2 x1 + (* - (* + (y1 * x1 2 x2 * + 3 x0 * - (x3 * x2 x0 2 x2 * + 3 x1 * + (* + 33 x0 2^* x1 2^- (* - (y0 * - (* + 3 x3 x2 x1 + 4 x3 x0 + (* - (* x1 x1 3 x0 * + (* + (* x2 x2 2 x1 * + 3 x0 * + (* + (y0 2^* - (z3 * y3 3 x1 4 x2 * - 3 x0 * + (x3 * x1 x0 + 4 x2 * - (x2 * + x0 2^+ (* x1 x1 2 x0 * + (* + (y3 * 3 x3 x1 x0 + 4 x3 * + (* x0 3 x1 4 x2 * - (* + (x2 * + x1 2^+ (* x0 x0 2 x1 * + (* + (y2 * + x3 x0 3 x3 x2 + (* + (* x1 x0 3 x2 x1 + (* + (* - (y1 * - x3 x1 - 3 x2 3 x3 * + (* + (* - x0 2 x1 * + (x2 * + x1 2 x1 * 3 x0 * + (* + 3 x0 2^* + (y0 * + (* - 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(* y1 * x3 x3 2 x2 * + 3 x1 x0 + (* + (* 3 x2 x2 x0 + 3 x1 * + (* 4 x0 2^3 x1 2^* - (* + (* + (y0 * + (* + x3 3 x1 3 x0 * + x3 + (* 2 x2 * + (* x2 x2 3 x1 x0 + (* + (* + 12 x1 * x1 x0 + (* - (y0 2^* + (z1 * + y3 3 x1 3 x2 * + 4 x0 * - (x3 * x2 2^+ x0 x1 4 x0 * - (* + (* 2 x1 * 3 x0 * + (x2 * + x1 2^+ (y3 * x3 x1 - 3 x0 3 x3 * + (* + (* - x2 x0 3 x2 x1 + (* + (* + 2 x1 * x1 x0 + (* + (y2 * + x1 x2 3 x1 x0 + (* + (* x3 x2 3 x3 x0 + (* + (* - (y1 * + 3 x3 x2 x1 + 4 x3 * + (* x1 x1 3 x0 * + (* + 12 x0 2^* - (* x2 x2 2 x1 * + 3 x0 * + (* + (y0 * + (* y2 x1 x0 3 x2 x1 + (* + (* x3 x0 3 x3 x2 + (* + (* - (y2 * x3 x1 2 x3 x0 + (* + 3 x2 * + (* x2 x0 3 x2 * + (* + 3 x1 * x0 3 x1 * + (* - (y1 * - x1 x2 3 x1 x0 + (* + (* x3 x2 3 x3 x0 + (* + (* - (y0 * + (* + y1 34 x0 * x1 x0 + (* x2 x2 x0 + 3 x1 * + (* - (* x3 x3 2 x2 * + 3 x1 x0 + (* + (* - (y1 * x3 3 x3 x1 + 3 x0 * + (* 2 x2 * + (* x2 x2 3 x1 x0 + (* + (* + 123 x0 2^* x1 2^- (* - (y0 * - (* + 12 x3 x3 3 x0 * + (* - x1 x1 3 x0 * + (* + (* y0 2^* - (z0 * + 720 / : IxG IxG0 Vol yG 2^* - : IyG IyG0 Vol xG 2^* - : IxyG IxyG0 Vol xG * yG * - : Vol xG yG 031 mat IxG0 IyG0 IxyG0 31 mat IxG IyG IxyG 31 mat 14 mat 111 line :

XYZ 0020121 - 121 - 0243 mat :

Vol x.G y.G xx 31 mat I.xG0 I.yG0 I.xyG0 31 mat I.xG I.yG I.xyG 31 mat 14 mat XYZ RGeoPH : 2 0.5 - 0.5 031 mat 0.6667 0.6667 0.5 - 31 mat 0.1667 0.1667 031 mat 14 mat

21 * 13^* 12 / 0.1667