Surfaces {continuous surface} can have tangent plane and normal line at all points.
Truncated solids can have parallel plane sections {frustum}.
Surfaces {hyperboloid} can have cross-sections that are hyperbolas.
If surfaces {isometric surface} bend without stretching and keep one-to-one correspondence, curvature and all other properties stay the same.
Focal surfaces of systems of second-order rays are fourth-degree and class-four surfaces {Kummer surface}. Fresnel wave surfaces are special cases.
Solids can have plane parallel faces {lamina} that are small distance apart compared to face length.
Surfaces {paraboloid} can have sections that are parabolas. x^2 / a^2 + y^2 / b^2 = 2*c*z {elliptic paraboloid}, where a b c are axes. Elliptic paraboloid with a = b is parabola rotated about its z-axis. x^2 / a^2 - y^2 / b^2 = 2*c*z {hyperbolic paraboloid}, where a b c are axes.
Straight lines {rectilinear generator} can generate surfaces {ruled surface}| by translation in one direction, making lines at equal intervals. If there are two distinct generators, surfaces are doubly ruled. No generator can make skew surfaces.
Surfaces {smooth surface} can have no irregularities. Objects on smooth surfaces move only in direction tangent to surface.
Surfaces {unilateral surface} can have one side.
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Date Modified: 2022.0225