424f0c1b-d14d-493a-bbb0-1bb361491db3 27 6 12 decimal

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Direction Cosine ... solve distance in space

DirectionCosines . . .

Is an important concept in space geometry. It enables plotting

the 3D plane(x,y) normal to the 3D solid of revolution wrt user

specified angular directions [u,v].

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a 1 : b 2 : c 1 : 13 mat

u v E a u cos * v sin * b u sin * v sin * c v cos * 31 mat :

u v Plan u sin v sin * u sin v cos * u cos 31 mat :

ellipsoid u v E 02 π * π - 01212 CreateMesh :

u π 4 / : v π 3 / : 12 mat

u v Plan 0.612372436 0.353553391 0.707106781 31 mat

evaluate SYMBOLIC step ... plug-in solve(,≡0) x y sol step 0.612372 0.353553 0.707107 31 mat transpose x y z 31 mat * : 3204124 x * 117851 y * + (* 707107 z * + 1000000 / 0 ≡ z solve maple 21 line :

12 / 3 sqrt * x * - 12 / y * -

x y P x y 12 / 3 sqrt * x * - 12 / y * - 31 mat :

x y sol 3204124 x * 117851 y * + (* 707107 / -

11 P 11 1.366025 - 31 mat

x y plane x y x y sol 31 mat :

plane x y plane 2 - 2 π - π 1010 CreateMesh :

ellipsoid plane 2 1 sys

u 11 E : 0.454649 1.416147 0.540302 31 mat

v 11 plane : 11 1.366024 - 31 mat

point distance in space
point on plane <=> solid u v dist u v - (2^(vectorize sum sqrt :

u v dist 2.025997

v 1 el u 1 el - (2^v 2 el u 2 el - (2^+ v 3 el u 3 el - (2^+ sqrt 2.025997

X 23131 mat :

Y 85 - 031 mat :

random points in 3Dspace Y 1 el X 1 el - (2^Y 2 el X 2 el - (2^+ Y 3 el X 3 el - (2^+ sqrt 10.05

P X transpose Y transpose stack (:

Ellipse normal to the plane

x aa / (2^y bb / (2^+ z cc / (2^+ 1 ≡ z solve maple aa x - (aa x + (* bb 2^* y 2^aa 2^* - sqrt cc * bb aa * / aa x - (aa x + (* bb 2^* y 2^aa 2^* - sqrt cc * bb aa * / - 21 mat

a 1 : b 2 : c 1 : 13 mat

x y Ellipse0 x y a x - (a x + (* b 2^* y 2^a 2^* - sqrt c * b a * / abs 31 mat :

x y Ellipse1 x y a x - (a x + (* b 2^* y 2^a 2^* - sqrt c * b a * / abs - 31 mat :

ellipse0 x y Ellipse0 1 - 1 0.00001 - 0.00001 4040 CreateMesh : ellipse1 x y Ellipse1 1 - 1 0.00001 - 0.00001 4040 CreateMesh : 21 sys

zoom 7.5 :

ellipse0 zoom * ellipse1 zoom * 2 1 sys ellipse0 zoom * ellipse1 zoom * plane zoom * 0.5 * 3 1 sys ellipsoid ellipse0 ellipse1 3 1 sys

n ellipse1 rows : 9560

ellipse ellipse0 ellipse1 stack :

ellipsoid uu vv E 0 3.125 0 3.125 1212 CreateMesh :

Remove left over stack junction

ellipsoid ellipse 2 1 sys