Write a program to draw a cubic Bezier curve.
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The document outlines an experiment to programmatically draw a cubic Bézier curve using MATLAB 13. It describes the theoretical basis for the curve defined by four control points, with specific calculations and the program code for generating the Bézier curve based on user-inputted coordinates. Additionally, it explains how to recover control points based on certain values along the curve.
![EXPERIMENT- 6
Objective: - Write a program to draw a cubic Bezier curve.
Software Used: - MATLAB 13
Theory: Four points P0, P1, P2 and P3 in the plane or in higher-dimensional space define a
cubic Bézier curve. The curve starts at P0 going toward P1 and arrives at P3 coming from the
direction of P2. Usually, it will not pass through P1 or P2; these points are only there to provide
directional information. The distance between P0 and P1 determines "how long" the curve moves
into direction P2 before turning towards P3. Writing BPi,Pj,Pk(t) for the quadratic Bézier curve
defined by points Pi , Pj , and Pk, the cubic Bézier curve can be defined as a linear combination
of two quadratic Bézier curves:
The explicit form of the curve is:
For some choices of P1 and P2 the curve may intersect itself, or contain a cusp. Any series of
any 4 distinct points can be converted to a cubic Bézier curve that goes through all 4 points in
order. Given the starting and ending point of some cubic Bézier curve, and the points along the
curve corresponding to t = 1/3 and t = 2/3, the control points for the original Bézier curve can be
recovered.[4] The derivative of the cubic Bézier curve with respect to t is
The second derivative of the Bézier curve with respect to t is
Program:
for i = 1:4
x(i)= input('Enter x coordinate: ');
y(i)= input('Enter y coordinate: ');
end
t=1;
for u = 0.0:0.01:1.0
Bez0(t) = (1-u).^3;
Bez1(t) = (3*u)*(1-u).^2;
Bez2(t) = 3 * (u.^2)*(1-u);
Bez3(t) = (1-u).^3;
X(t) = Bez0(t)*x(1)+Bez1(t)*x(2)+Bez2(t)*x(3)+Bez3(t)*x(4);](https://image.slidesharecdn.com/6beziercurve-170225083051/85/Write-a-program-to-draw-a-cubic-Bezier-curve-1-320.jpg)
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Write a program to draw a cubic Bezier curve.
- 1. EXPERIMENT- 6 Objective: - Write a program to draw a cubic Bezier curve. Software Used: - MATLAB 13 Theory: Four points P0, P1, P2 and P3 in the plane or in higher-dimensional space define a cubic Bézier curve. The curve starts at P0 going toward P1 and arrives at P3 coming from the direction of P2. Usually, it will not pass through P1 or P2; these points are only there to provide directional information. The distance between P0 and P1 determines "how long" the curve moves into direction P2 before turning towards P3. Writing BPi,Pj,Pk(t) for the quadratic Bézier curve defined by points Pi , Pj , and Pk, the cubic Bézier curve can be defined as a linear combination of two quadratic Bézier curves: The explicit form of the curve is: For some choices of P1 and P2 the curve may intersect itself, or contain a cusp. Any series of any 4 distinct points can be converted to a cubic Bézier curve that goes through all 4 points in order. Given the starting and ending point of some cubic Bézier curve, and the points along the curve corresponding to t = 1/3 and t = 2/3, the control points for the original Bézier curve can be recovered.[4] The derivative of the cubic Bézier curve with respect to t is The second derivative of the Bézier curve with respect to t is Program: for i = 1:4 x(i)= input('Enter x coordinate: '); y(i)= input('Enter y coordinate: '); end t=1; for u = 0.0:0.01:1.0 Bez0(t) = (1-u).^3; Bez1(t) = (3*u)*(1-u).^2; Bez2(t) = 3 * (u.^2)*(1-u); Bez3(t) = (1-u).^3; X(t) = Bez0(t)*x(1)+Bez1(t)*x(2)+Bez2(t)*x(3)+Bez3(t)*x(4);
- 2. Y(t) = Bez0(t)*y(1)+Bez1(t)*y(2)+Bez2(t)*y(3)+Bez3(t)*y(4); t = t+1; end subplot(3,2,1);plot(Bez0); subplot(3,2,2);plot(Bez1); subplot(3,2,3);plot(Bez2); subplot(3,2,4);plot(Bez3); subplot(3,2,5);plot(x,y,'--rs',X,Y); Output: Enter x coordinate: 2 Enter y coordinate: 4 Enter x coordinate: 1 Enter y coordinate: 2 Enter x coordinate: 3 Enter y coordinate: 6 Enter x coordinate: 4 Enter y coordinate: 8