Alexey Ivanov

5 years, 53 days

## The distance from the point to the surfa...

Maple 15

The distance from the point to the surface easily calculated using the NLPSolve of Optimization package. If the point is not special, we will find for it a point on the surface, the distance between these two points is the shortest between the selected point and the surface.
Two examples:  the implicit surface and the parametric surface.
To test, we restore the normals from the  calculated  points (red) by using analytical equations.
DISTANCE_TO_SURFACE.mw

## Rolling without slipping on a non-orient...

Maple 15

The Möbius strip  Mobius_strip_rolling.mw

Variants :

The line and the curve on the surface.

## Second-order curve in 3d...

Maple 15

Parametric equation of second-order curve in 3d. Draghilev method.
PLAN_CURVE_3d_1.mw
Examples:
x1^2+x1*x3+13*x2^2+x3-1=0;
x1+x2+x3=0;

x1^2+0.1*x2^2+x3^2-9=0;
x1+3*x3+1=0;

x1^2-0.1*x2^2+x3^2-9=0;
x1+3*x3+1=0;

## Circle in 3d ...

Maple 15

Parametric equation of a circle in 3d by three points. Draghilev method.

CIRCLE_3_POINTS_geom3d_2.mw

## Isolation of sides of the surface on the...

Maple 15

One way is coloring a surface on both sides. We build equidistant surface with very small radius and stain the equidistant surface in color different from the color of the original surface.
Examples coloring of surfaces on both sides.  Radius equal to abs (0.0001).
x3-0.5*exp(sin(x1+2.5*x2+x3))=0;
(x1^2+x2^2-0.4)^2+(x3+sin(x1*x2+x3))^4-0.1=0;

2_COLORS.mw

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