MeshPlot

4525fe51-6c4a-4baf-a182-1193d5322ed0 31 4 5 decimal

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

MeshPlot

2 f U V MeshPlot n.p 5 : n.u U length 1 - : n.v V length 1 - : r 1 : 14 mat M n.p n.u * n.v * n.u n.v 1 - (* + 3 matrix : F n.u 1 + n.v 1 + matrix : u 1 n.u 1 + (range v 1 n.v 1 + (range F u v el U u el V v el f transpose eval : for for u 1 n.u range v 1 n.v range c 13 range M r c el F u v el c el : M r 1 + c el F u v 1 + el c el : M r 2 + c el F u 1 + v 1 + el c el : M r 3 + c el F u 1 + v el c el : M r 4 + c el F u v el c el : 51 line for r r n.p + : 21 line for k 0 n.v 2 - (range n u 1 - (n.p n.v * n.v + 1 - (* n.p v 1 - (* + k n.p * - : c 13 range M r c el M n c el : for r r 1 + : 31 line for 21 line for M 61 line :

speeds cals by ~10 U u el V v el f transpose eval

NOT needed M eval

2 f u.1 u.2 v.1 v.2 n.u n.v MeshPlot u# v# f u.1 u.2 u.1 - n.u 1 - / 0 n.u 1 - (range (* + v.1 v.2 v.1 - n.v 1 - / 0 n.v 1 - (range (* + MeshPlot :

Kleinsche Flasche Euler Rotation

angle ° symbol ∠

EulerRot(v) returns the Euler rotation matrix ... Euler is aviation style,i.e: NOT commutative. ∠ EulerRot 1000 ∠ 1 el cos ∠ 1 el sin - 0 ∠ 1 el sin ∠ 1 el cos 33 mat ∠ 2 el cos 0 ∠ 2 el sin 010 ∠ 2 el sin - 0 ∠ 2 el cos 33 mat * ∠ 3 el cos ∠ 3 el sin - 0 ∠ 3 el sin ∠ 3 el cos 000133 mat * :

M Proj.2 M 1 M rows range 12 range el :

K v Proj.2 K v EulerRot * Proj.2 :

x y z Axis3D 000 x 000000 y 000000 z 00073 mat :

Torus Example

Toroid u v T R r u cos * + (v cos * R r u cos * + (v sin * r u sin * 31 mat :

R 6 :

r 2 :

Ω 30 ° * 45 ° * 60 ° * 13 mat :

γ Ω EulerRot :

A 234 Axis3D :

T u v T 032 / π * 032 / π * 1818 MeshPlot :

T Ω Proj.2

P T 2 col T 3 col augment :

θ rot θ cos θ sin - θ sin θ cos 22 mat :

θ π - 4 / :

θ 0.7854 -

Rot P θ rot * :

3D Plot

3D pre-oriented Euler

T γ * A 2 1 sys

2D Plot ... user orient

Rot A Proj.2 2 1 sys

Alvaro

t0 1 time :

Q u v T 02 π * 02 π * 3434 CreateMesh :

1 time t0 - 7 s *

t0 1 time :

T u v T 02 π * 3502 π * 35 MeshPlot :

1 time t0 - 13 s *

Q 800 7.8638 1.47 0 7.8303 1.4637 0.3675 7.9659 0 0.3675 800 7.8638 1.47 0 7.4598 2.8899 0 7.428 2.8776 0.3675 7.8303 1.4637 0.3675 7.8638 1.47 0 7.4598 2.8899 0 6.8017 4.2115 0 6.7728 4.1935 0.3675 7.428 2.8776 0.3675 7.4598 2.8899 0 6.8017 4.2115 0 5.9121 5.3896 0 5.8869 5.3666 0.3675 6.7728 4.1935 0.3675 6.8017 4.2115 0 5.9121 5.3896 0 4.8211 6.3841 0 4.8006 6.357 0.3675 233 mat

T 7.2295 - 3.4255 - 0 6.6612 - 4.4305 0 5.6159 - 3.7352 1.8562 6.0951 - 2.8879 - 1.8562 7.2295 - 3.4255 - 0 6.6612 - 4.4305 0 0.3642 7.9917 0 0.3071 6.7377 1.8562 5.6159 - 3.7352 1.8562 6.6612 - 4.4305 0 0.3642 7.9917 0 7.0366 3.8062 0 5.9324 3.2089 1.8562 0.3071 6.7377 1.8562 0.3642 7.9917 0 7.0366 3.8062 0 6.888 4.0689 - 0 5.8071 3.4304 - 1.8562 5.9324 3.2089 1.8562 7.0366 3.8062 0 6.888 4.0689 - 0 0.0625 7.9998 - 0 0.0527 6.7445 - 1.8562 233 mat