Pyramid Spline ... Spool to File

ed88493d-415f-40f5-a042-855d0c4fb3df 3 15 12 decimal

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

N 10 : α 4 : 13 mat

MCD 00000000000000000000001111111111111111111001222222222222222221001233333333333333321001234444444444444321001234555555555554321001234566666666654321001234567777777654321001234567888887654321001234567899987654321001234567891098765432100123456789998765432100123456788888765432100123456777777765432100123456666666665432100123455555555555432100123444444444444432100123333333333333332100122222222222222222100111111111111111111100000000000000000000002121 mat :

u v f u α N * u - v α N * v - 41 mat min Ceil :

x y 12 mat 3 ± ≡

f Pyramid Spline ... Spool to File

x y M Spline A M 112 M cols submatrix : B M 2 M rows 11 submatrix : C M 2 M rows 2 M cols submatrix : j 1 A length 2 range CC j el B C 1 C rows j j submatrix y linterp : for A transpose CC x ainterp 51 line :

Pyr 012345678910111213141516171819201111111111111111111102122222222222222222103123333333333333332104123444444444444432105123455555555555432106123456666666665432107123456777777765432108123456788888765432109123456789998765432101012345678910987654321011123456789998765432101212345678888876543210131234567777777654321014123456666666665432101512345555555555543210161234444444444444321017123333333333333332101812222222222222222210191111111111111111111020000000000000000000002121 mat :

u v q u v u v Pyr Spline 31 mat :

Pyramid u v q 0200202121 CreateMesh 3 round vectorize :

CWD C:\SmathFile CurrentDirectory :

Pyramid CWD Pyramid wfile 1

Pyramid CWD Pyramid rfile :

0.5 Pyramid *

Quaternions system.
native modulo 6 permute
go to permute oder 'j' α 0.75 : β 0.25 - : 12 mat vectormodulo 1 : (select modulo[1,2] ≡ 21 sys

Quaternion

1. Instruct/code the solver a b GivenFind a b FindRoot :

Solutions from the GivenFind solver are in lexicographic order wrt "init".

init 1 :

2. System to solve v1 p q + r - 0 ≡ p 2^q 2^+ r 2^+ 1 ≡ α p * β r * + 0 ≡ 31 mat :_v2 p init ≡ q init ≡ r init ≡ 31 mat : 13 mat

Observe:

1. init [10e-15] => col(modulo,1)

2. init [1] => col(modulo,2)

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solutions p q r 31 mat ≡

Quaternion v1 v2 GivenFind : 0.267 - 0.535 - 0.802 - 31 mat

p q r 31 mat 0.267 - 0.535 - 0.802 - 31 mat

3. Define the Quaternion "modulo"
... and the Quaternion vector modulo 2 β 2^* 2 β * α * + 2 α 2^* + sqrt :

V β - modulo / β modulo / β α + (modulo / β α + (- modulo / α modulo / α - modulo / 32 mat : 0.2673 0.2673 - 0.5345 0.5345 - 0.8018 0.8018 - 32 mat

4. Create the Quaternion vector ω V vectormodulo col V 11 el stack :

ω 0.2673 0.5345 0.8018 0.2673 41 mat

Euclidean norm => Quaternion vector ω 1 el 2^ω 2 el 2^+ ω 3 el 2^+ ω 4 el 2^+ sqrt 1.035

ω norme 1.035

# norme Euclidean norm ≡

5. Define the "UnitV", apply to 'q' q ω ω norme / : 0.2582 0.5164 0.7746 0.2582 41 mat

q <= that goes in 'quat' converter

6. The rotation 'quat' converter q quat 12 q 3 el (2^* - 2 q 4 el (2^* - 2 q 2 el * q 3 el * 2 q 1 el * q 4 el * - 2 q 1 el * q 3 el * 2 q 2 el * q 4 el * + 2 q 1 el * q 4 el * 2 q 2 el * q 3 el * + 12 q 2 el (2^* - 2 q 4 el (2^* - 2 q 1 el * q 2 el * - 2 q 3 el * q 4 el * + 2 q 1 el * q 3 el * - 2 q 4 el * q 2 el * + 2 q 1 el * q 2 el * 2 q 3 el * q 4 el * + 12 q 2 el (2^* - 2 q 3 el (2^* - 33 mat :

Permute

a q 1 el : b q 2 el : c q 3 el : d q 4 el : 14 mat

Permute  [a,b,c,d]... = 24 ... p a b c d 41 mat a b d c 41 mat a c b d 41 mat a c d b 41 mat a d b c 41 mat a d c b 41 mat b a c d 41 mat b a d c 41 mat b c a d 41 mat b c d a 41 mat b d a c 41 mat b d c a 41 mat c a b d 41 mat c a d b 41 mat c b a d 41 mat c b d a 41 mat c d a b 41 mat c d b a 41 mat d a b c 41 mat d a c b 41 mat d b a c 41 mat d b c a 41 mat d c a b 41 mat d c b a 41 mat 124 mat :

p 0.258 0.516 0.775 0.258 41 mat 0.258 0.516 0.258 0.775 41 mat 0.258 0.775 0.516 0.258 41 mat 0.258 0.775 0.258 0.516 41 mat 0.258 0.258 0.516 0.775 41 mat 0.258 0.258 0.775 0.516 41 mat 0.516 0.258 0.775 0.258 41 mat 17 mat

permuted rotaion 1...24 j 24 :

q p 1 j el :

0.5 Pyramid * q quat *

Pyramid CWD Pyramid rfile :

mouse rotation works well ... but NO export 'rot matrix'...

0.5 Pyramid *

q quat 0.333 0.667 0.667 0.933 0.333 - 0.133 - 0.133 0.667 0.733 - 33 mat

Pyramid Construction

N 10 : α 4 : 13 mat

u v f u α N * u - v α N * v - 41 mat min Ceil :

u v Clear 1

P u 010 range : v 010 range : r 1 : i 1 u rows range c 1 : j 1 v rows range M r c el u i el v j el f : c c 1 + : 21 line for r r 1 + : 31 line for 21 line M 41 line :

sub u 010 range : v 100 range : r 1 : i 1 u rows range c 1 : j 1 v rows range M r c el u i el v j el f : c c 1 + : 21 line for r r 1 + : 31 line for 21 line M 111 range 211 range el 41 line :

New is sanity Mathcad.
Top row, left column
are manually filled 
for the Spline mesh. A P sub augment : Asub A 101 range 121 range el : New A Asub stack : 31 sys