P M Dearing

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0 years, 147 days

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These are questions asked by P M Dearing

Given the center x1 of a circle in R^2 with radius d12, and a point p2 on the circle, so that d12=||p2-x1||, denote the points on the line segment from x1 to p2 as x1(t) = x1+t*v12, with t=0..d12, and v12 =( p2-x1)/d12.  I want to animate the points x1(t) moving along the line segment from x1 to p2 and the corresponding circles of decreasing radius, with center x(t) and radius d12-t, so that p2 remains on the circle.

I can animate the points along the line segment from x1 to p2 using ‘style=point, symbol=solidcircle’.

I would like to use plottools-circle, to plot the circles. I have also tried the following type commands for the circles of decreasing radius.

Plot([x1(1)+t*v12(1)+(d12-t)*cos(theta)*v12(1)+ (d12-t)*sin(theta)*u12(1), x1(2)+ +t*v12(2)+(d12-t)*d12*cos(theta)*v12(2)+(d12-t)*sin(theta)*u12(2), theta=0..2*PI]

where u12 is a unit vector orthogonal to v12.

I have not been able to combine the two plots into an animation. Thank you

Using the parametric representation of a circle in 2 dimensions:  c + r*cos(t)*v + r*sin(t)*u, t = 0..2*Pi,  where c is the center, r is the radius, v and u are orthogonal unit vectors, I want to animate the circle for r = r1..r2.

Example:

animate(plot, [c+r*cos(t)+r*sin(t),t=0..6.3],r=5..10);

I don't understand why this doesn't work!!  

Thank you

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