WHAT NEEDS TO BE DONE IS:

1. You must construct a program that allows the user, by clicking with the mouse on the screen, to create control points, once the points are entered, the Bézier curve determined by the points must be created.

2. The user may determine arbitrary shapes with the mouse in such a way that figures such as those shown in the document can be created (trolley, letter, vessel, etc.)

3. The arbitrary drawing may be made with Bézier curves of degrees 2, 3, and 4. In such a way that each (2, 3, and 4) point is created a Bézier curve.

4. Once the shape has been created, the user can drag with the mouse any of the control points and the program must allow the curve to follow the chosen control point.

5. Once the figure has been formed with the Bezier curves, this figure may be completed

PD: IN ANY programming language.

Transcribed Image Text:

● A Bézier curve can be described using a mathematical formula. Given the coordinates of the control points Pi: the first control point has the coordinates P1 = (x1, y1), the second: P2 = (x2, y2), and so on, the coordinates of the curve are described by the equation that depends on the parameter t of the segment [0,1]. The formula for a 2-point curve: P = (1-t) P₁+ tP2 ● For 3 control points: P =(1-t) ²P₁ + 2(1-t) tP₂ + t²P3 For 4 control points: P = (1-t) ³P₁ + 3(1-t)²tP₂ +3 (1-t)t²P3 + t³P4 These are the vector equations. In other words, we can put x and y instead of P to get the corresponding coordinates. ● A Bézier curve can be described using a mathematical formula. Given the coordinates of the control points Pi: the first control point has the coordinates P1 = (x1, y1), the second: P2 = (x2, y2), and so on, the coordinates of the curve are described by the equation that depends on the parameter t of the segment [0,1]. The formula for a 2-point curve: P = (1-t) P₁+ tP2 ● For 3 control points: P =(1-t) ²P₁ + 2(1-t) tP₂ + t²P3 For 4 control points: P = (1-t) ³P₁ + 3(1-t)²tP₂ +3 (1-t)t²P3 + t³P4 These are the vector equations. In other words, we can put x and y instead of P to get the corresponding coordinates.

Answer rating: 100% (QA)

Yes you are correct Bzier curves can be described using mathematical formulas that depend on the coo... View the full answer