As abstract as this question is, a detailed help is difficult.Hi, I need to draw a circle on plane. I have a center point, radius and a plane equitation ax+by+cz + d = 0does anyone have any ideas to get me started? thanks !!!!
Thank you !!!! What do f, g, h vars represent?As abstract as this question is, a detailed help is difficult.
First gave you checked to see if the centre you have is actually on that plane?
If \(\displaystyle \mathfrak{C}(p,q,r)\) is the centre then \(\displaystyle ap+bq+cr+d=0\) the center is on the plane.
Lets say \(\displaystyle R\) is the radius.
The circle is \(\displaystyle \left\{(f,g,h) : (p-f)^2+(q-g)^2+(r-h)^2=R^2\right\}\) and the vectors \(\displaystyle \left<a,b,c\right>\cdot\left<p-f,q-g,r-h\right>=0.\).
The is a vector from the centre to a point of the circle is perpendicular to the normal of the plane and has length \(\displaystyle R\).
Well they are coordinates of points on the circle.Thank you !!!! What do f, g, h vars represent?
I think that's "coordinates".Well they are confidantes of points on the circle.
Start with your equation [MATH]ax+by+cz = d[/MATH] and your given point [MATH](p,q,r)[/MATH] on the plane. A normal vector to your plane is [MATH]\vec N = \langle a,b,c \rangle.[/MATH]. Create any nonzero vector [MATH]\vec U[/MATH] perpendicular to [MATH]\vec N[/MATH]. This is trivial. For example [MATH]\vec U = \langle -b, a, 0\rangle[/MATH] will work if [MATH]a[/MATH] and [MATH]b[/MATH] aren't [MATH]0[/MATH]. (If you can't find two nonzero coefficients your problem is trivial anyway). Create another vector [MATH]\vec V = \vec N \times \vec U[/MATH]. Now divide [MATH]\vec U[/MATH] and [MATH]\vec V[/MATH] by their lengths to make unit vectors [MATH]\hat u[/MATH] and [MATH]\hat v[/MATH]. These are perpendicular unit vectors in your plane. Then a circle of radius [MATH]R[/MATH] in your plane with [MATH](p,q,r)[/MATH] as center is
[MATH]\langle x,y,z \rangle= \langle p,q,r \rangle + \vec u R\cos t + \vec v R\sin t,~0 \le t \le 2\pi[/MATH],