Define a variable on a spline

Hey there,

My problem is, that I have a spline and I need to get a variable that follows the line.

n = 3;
n1 = n-1;
a = 20;             
b = 10;             
P = [0 b;0 0;a 0];
x = P(:,1);        
y = P(:,2);         
T = 20;           

syms t
B = bernsteinMatrix(n1,t);
bezierCurve = simplify(B*P);  
fplot(bezierCurve(1), bezierCurve(2), [0, 1])  
axis equal
grid on
hold on
scatter(x,y,'filled')
hold off

arclen = arclength(px,py) %You need the arclength function there for

In this example the variable needs to have the value 0 on the point (0 10) and it needs to have the value of the arclength in point (20 0)

I hope you guys have some great ideas.

Thank You!

Answer 1

[Matt J]

n = 3;
n1 = n-1;
a = 20;             
b = 10;             
P = [0 b;0 0;a 0];
x = P(:,1);        
y = P(:,2);         
T = 20;           
syms t
assume(t>=0 & t<=1)

B = bernsteinMatrix(n1,t);
bezierCurve = simplify(B*P);  

arclength(t)=int(norm(diff(bezierCurve)),0,t)

arclength(t) = 

double(arclength(0))

ans = 0

double(arclength(1))

ans = 24.8865

Answer 2

[Torsten]

n = 3;
n1 = n-1;
a = 20;             
b = 10;             
P = [0 b;0 0;a 0];
x = P(:,1);        
y = P(:,2);         
T = 20;           

syms t
B = bernsteinMatrix(n1,t);
bezierCurve = simplify(B*P);  
fun = int(sqrt(diff(bezierCurve(1),t)^2+diff(bezierCurve(2),t)^2),0,t);
subs(fun,t,0)

ans = 

0

subs(fun,t,1)  % Arclength of curve between the two points (0 10) and (20 0)

ans =