arclengthNumeric.mws

arclengthNumeric - výpočet délky oblouku křivky nahrazením lomennou čarou

Calling Sequence

 arclengthNumeric(X(t),t,a,b,n)

arclengthNumeric(X(t),t,a,b)

arclengthNumeric(X(t),t)
arclengthNumeric([x(t), y(t), z(t)],t,a,b,n)

Parameters

X(t)  vektorová funkce popisující křivku v Euklidovském prostoru 2D ( X(t) = [x(t), y(t)]  ), nebo pro 3D X(t) = [x(t), y(t), z(t)] .

    t    parametr křivky

a,b, ..interval parametru, t=a..b. Pokud tyto hodnoty nenastavíte, bude interval parametru nastaven na <0,1>.

   n ...počet stran lomenné křivky. Pokud jeho hodnotu nezadáte, bude automaticky nastavena na 20. Provedením příkazu je jeho hodnota uložena do globální proměnné NumElements . V proměnné Vertex  je pole vrcholů lomenné čáry.

Description

Examples

Nejprve je třeba nastavit cestu, kde máte uloženou knihovnu "diffgeometry", např

>    restart;

>    libname:=libname,"D:/Sarka/Maple/diffgeometry/libsarka";

libname :=

>    with(diffgeometry);

[AsymptoticDir, D1, D2, E, EFG, F, G, GaussCurvature, L, LMN, M, MeanCurvature, N, PrincipalMatrix, arclength, arclengthNumeric, curvature, dp, dupin, frenet, l, m, n, normalize, nrm, revolve, screw, t...
[AsymptoticDir, D1, D2, E, EFG, F, G, GaussCurvature, L, LMN, M, MeanCurvature, N, PrincipalMatrix, arclength, arclengthNumeric, curvature, dp, dupin, frenet, l, m, n, normalize, nrm, revolve, screw, t...

V rovině zadáme parametricky jednotkovou kružnici

>    k:=[cos(t),sin(t)];

k := [cos(t), sin(t)]

Počítáme délku celé kružnice, tj t=0..2*Pi. Kružnici nahradíme pravidelným 10-úhelníkem

>    arclengthNumeric(k,t,0,2*Pi,10);pocetstran:=NumElements;
vrcholy:=eval(Vertex);

6.180339887

pocetstran := 10

vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...
vrcholy := ARRAY([0 .. 10],[(0) = [cos(0), sin(0)], (1) = [cos(1/5*Pi), sin(1/5*Pi)], (2) = [cos(2/5*Pi), sin(2/5*Pi)], (3) = [cos(3/5*Pi), sin(3/5*Pi)], (4) = [cos(4/5*Pi), sin(4/5*Pi)], (5) = [cos(Pi...

Nakreslení lomenné čáry, která nahrazuje dannou kružnici

>    plot([seq(Vertex[i],i=0..NumElements)],scaling=constrained);

[Maple Plot]

Výpočet délky prostorové křivky. Vynecháme-li poslední parametr, je automaticky nastaven na 20.

>    arclengthNumeric([cos(t),sin(t),2*t],t,0,Pi);

`Počet stran lomenné čáry je nastaven na 20.`

7.023371356

>   

See Also

 , evalf  , int , diff , UsingPackages , with