I have a curve and a circle on x,y axes. I want to plot points on the curve and on the circle based on the “a”. The value of “a” should be {1/5,2/5,3/5,4/5} of the curve and the circle. Then, I want to connect those points on curve and the circle. I’ve been working on this for several days but still couldn’t found the solution.

Quad1 = {{-1, 0}, {0, 1}, {1, 0}};(*Define 3 control points for the polygon*)

Print[MatrixForm[Quad1]]

q1 = Graphics[BezierCurve[Quad1]]; (*Construct a Bezier Curve*)

a = BezierFunction[Quad1]

Show[Graphics[{Red, Point[Quad1], Green, Line[Quad1]}, Axes -> True],

ParametricPlot[a[t], {t, 0, 1}],

ParametricPlot[{{ Cos[t], Sin[t]}}, {t, 0, Pi},

PlotLegends -> “Expressions”, PlotStyle -> Orange,

PlotRange -> {0, 1}]]

a1 = a[1/5]

a2 = a[2/5]

a3 = a[3/5]

a4 = a[4/5]

=================

Firstly, what’s Quad1?

– Wjx

Sep 18 at 23:11

Quad1 is the control points for the bezier curve. (blue curve)

– NKamaru

Sep 18 at 23:40

=================

1 Answer

1

=================

Quad1 = {{-1, 0}, {0, 1}, {1, 0}};

a = BezierFunction[Quad1];

pts1 = a /@ Range[1/5, 4/5, 1/5];

pts2 = {Cos[#], Sin[#]} & /@

(Pi Range[4/5, 1/5, -1/5]);

Show[

ParametricPlot[{Cos[t], Sin[t]}, {t, 0, Pi}],

ParametricPlot[a[t], {t, 0, 1}],

Epilog -> {

AbsolutePointSize[6],

Green,

Line[Quad1],

Red,

Point[pts1],

Point[pts2],

Dashed,

Line /@ Transpose[{pts1, pts2}]}]