Plane parametric curve

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Plane path

t x r t cos * xo + : t y r t sin * yo + : 21 sys

t 02 π * lelt

Values

r 2 :

xo 2 - :

yo 3 :

Range parameter

T 02 π * (0.1 range :

T to to Δt + tf \0020\range ≡

Vectorial evaluation and plot

X T x vectorize : Y T y vectorize : 21 sys

X Y augment xo yo o 12 blue 1 5 mat 2 1 sys Rational Parametrization

Plane path (rational parametrization)

t x r 1 t 2^- 1 t 2^+ / * xo + : t y r 2 t * 1 t 2^+ / * yo + : 21 sys

t ∞ - ∞ ltlt

Values

r 2 :

xo 2 - :

yo 3 :

Range parameter

T 20 - 20 19.9 - range :

T to to Δt + tf \0020\range ≡

Vectorial evaluation and plot

X T x vectorize : Y T y vectorize : 21 sys

X Y augment xo yo o 12 blue 1 5 mat 2 1 sys Spatial parametric curve

Spatial path

t x t cos A 1 el xo - (* t sin B 1 el xo - (* + xo + : t y t cos A 2 el yo - (* t sin B 2 el yo - (* + yo + : t z t cos A 3 el zo - (* t sin B 3 el zo - (* + zo + : 31 sys

Circle centered at (xo,yo,zo) through A and B.

View rotation

Values

r 2 :

xo 2 - :

yo 3 :

zo 1 - :

γ 0.8232 - 0.4194 - 0.3827 0.5677 0.6187 - 0.543 0.009 0.6643 0.7474 33 mat :

A 22 - 513 mat :

B 71 - 113 mat :

Range parameter

T 02 π * (0.1 range :

k 1 T rows range :

X Y Z Clear 1

Always clear before defining matrix elments in this way.

Evaluation and plots

X k el T k el x : Y k el T k el y : Z k el T k el z : 31 sys

C X Y Z augment γ * eval :

Because we use vector elements inside x,y and z(t) we can't vectorize here.

P clr Point P γ * (1 el P γ * (2 el o 12 clr augment :

C 1 C rows 1 2 submatrix xo yo zo 1 3 mat blue Point A red Point B green Point 4 1 sys C