5. Write down a general Bezier curve of order 4 in parametric form. How many control...
1. (10 points) Find the parametric equation for a Bezier curve with five control points Po, P1, P2, P3, and P4.
The Bezier curve in the following figure is defined by 4 control points. P,-(0. O), Pi = (1, 1), P2 (3, 2), Ps- (4, 0). a) b) Find the equation of the Bezier curve Find the point on the curve at u 0.5 1 0
Find out polar form of the last control point of third Bezier curve of a hodograph of a degree 4 B-spline with knot vector [1 2 3 4 5 6 7 8 9 10 11 12].
Some laser printers use Bezier curves to represent letters and symbols. Experiment with different sets of control points until you find a Bezier curve that gives a good representation of the letter C. Find 4 sets of points (P0, P1, P2, P3) that when plugged into x= x0(1−u)^3 +3(x1)u(1−u)^2 + 3(x2)u^2(1−u) + (x3)u^3 y= y0(1−u)^3 + 3(y1)u(1−u)^2 + 3(y2)u^2(1−u) + (y3)u^3 Create a C shape
c. Now write the general solution in parametric form. x = X11 X2 X3 XA X5 = P + (vectors multiplied by free variables) (Fill in the particular vector p, then factor out any remaining free variables from your expression above.) (4 points) particular 1 X2 X3 II II X4 + X2 X5 + 0 0 LX6 0 X₂ X₂ X₃ X4 Xg X6 1 2 3 0 5 6 d. Write a vector equation equivalent to the reduced system:...
Write the parametric equations x=2siny=4cos0 in the given Cartesian form. y^2/16= with x0. Write the parametric equations x=2sin2y=5cos2 in the given Catesian form. y= with 0x2. Write the parametric equations x=4ety=8e−t as a function of x in Cartesian form. y= with x0. Write the parametric equations x = 2 sin 0, y = 4 cos 0, 0<O< in the given Cartesian form. = with x > 0. 16 Write the parametric equations x = 2 sin’e, y = 5 cos?...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
4. (a) Find and write down the general solution of the ODE 2y'-x^3=0 in the form of a power series about x = 0. Only include the first three non-zero terms in each of the two linearly independent solutions (in an interval I centered at x = 0) that you obtain. (b) Check that each of the two linearly independent solutions you found in part (a) individually satisfies the ODE, up through terms of order x^12
need help Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 Find the length of parametized curve given by a(t) -0t3 -3t2 + 6t, y(t)1t3 +3t2+ 0t, where t goes from zero to one. Hint: The speed is a quadratic polynomial with integer coefficients. A curve with polar equation 14 7sin θ + 50 cos θ represents a line. Write this line in the given Cartesian form Note: Your answer should be...
4. Tired from the long week, with the amusement park and the wok and dinner plate designs, you retreat to be in peace and study parametric equations. A curious leaflike curve called the "folium of Descartes" catches your eye; it is defined by the parametric equations 3t 3t2 (a) (4 points) Show that if the point (a, b) lies on the curve, then so does (b, a); that is, the curve is symmetric with respect to the line y a....