Some geometric calculations
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Line
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[a, b, c]for$$ax+by+c=0$$ , where$$\sqrt{a^2+b^2}=1$$
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Circle
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[[a, b], r, [0.0, 0.0, 1.0, 0.0]]for$$(x-a)^2+(y-b)^2=r^2$$ - The last term,
[0.0, 0.0, 1.0, 0.0]], means that the circle lies in the plane$$z=0$$ , which is ignorable
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- Line
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[[a, b, c], [r, s, t]]for$$x=a+rk$$ $$y=b+sk$$ $$z=c+tk$$ , where$$\sqrt{r^2+s^2+t^2}=1,k\in\mathbb{R}$$
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- Plane
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[a, b, c, d]for$$ax+by+cz+d=0$$ , where$$\sqrt{a^2+b^2+c^2}=1$$
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- Circle
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[[x_c, y_c, z_c], r, [a, b, c, d]]for circle lies in plane[a, b, c, d], center at[x_c, y_c, z_c]and with radiusr
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- Sphere
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[[a, b, c], r]for sphere center at[a, b, c]and with radiusr
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- Cylinder
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[[a, b, c], h, r, [nx, ny, nz]]where-
[a, b, c]is the center of the base circle in 3D space -
handrare the height and the radius of the cylinder, respectively -
[nx, ny, nz]is the direction vector of the cylinder's direction axis
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