1. Graph the Bzier curve with control points Po(15,5), P (20, 42), P (50, 48), and...

 

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1. Graph the Bézier curve with control points Po(15,5), P₁ (20, 42), P₂ (50, 48), and P3 (40, 1). On the same plane, graph the line segments PoP1, P1P2, and P2P3. Include this graph as your solution, and include all labels on the graph. Notice that P₁ and P2 do not lie on the Bézier curve. To complete this question in Desmos, type the following into the graphing calculator: (xo (1 t)³ + 3x₁t(1 – t)² + 3x₂t²(1 – t) + x3t³, yo(1 – t)³ + 3y₁t(1 – t)² + 3y₂t² (1 – t) + y3t³) 2. 3. 4. Press enter. This will create sliders for the control points. These sliders also allow for the able to enter values. To label points, enter the point in another line and check the box beside "label". To provide clearer labels, enter desired label in the provided line. This method will allow you to easily manipulate these parametric equations for future questions. Prove that the tangent line of the Bézier at Po passes through P₁ and the tangent line at P3 passes through P₂. By adjusting the control points of the Bézier curve provided in Question 1, create a loop. Using two Bézier curves that share a control point, create a reasonable representation of the number 3. That is, the first Bézier curve will have control points Po through P3, and the second Bézier curve will have control points P3 through P6, where P3 is the same control point on both curves. 1. Graph the Bézier curve with control points Po(15,5), P₁ (20, 42), P₂ (50, 48), and P3 (40, 1). On the same plane, graph the line segments PoP1, P1P2, and P2P3. Include this graph as your solution, and include all labels on the graph. Notice that P₁ and P2 do not lie on the Bézier curve. To complete this question in Desmos, type the following into the graphing calculator: (xo (1 t)³ + 3x₁t(1 – t)² + 3x₂t²(1 – t) + x3t³, yo(1 – t)³ + 3y₁t(1 – t)² + 3y₂t² (1 – t) + y3t³) 2. 3. 4. Press enter. This will create sliders for the control points. These sliders also allow for the able to enter values. To label points, enter the point in another line and check the box beside "label". To provide clearer labels, enter desired label in the provided line. This method will allow you to easily manipulate these parametric equations for future questions. Prove that the tangent line of the Bézier at Po passes through P₁ and the tangent line at P3 passes through P₂. By adjusting the control points of the Bézier curve provided in Question 1, create a loop. Using two Bézier curves that share a control point, create a reasonable representation of the number 3. That is, the first Bézier curve will have control points Po through P3, and the second Bézier curve will have control points P3 through P6, where P3 is the same control point on both curves.

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Answer A cubic Benzero curve is defermined by four Control p... View the full answer