Alexey Ivanov

## 815 Reputation

8 years, 258 days
Russian Federation

## Purpose?...

@tomleslie   Here is the purpose: parametric equation of second-order curve in 3d.
For example, the first curve equations:
x1(s)= -135000000013/5000000000+(166055512773/10000000000)exp(s)+(101773194523/10000000000)exp(-s);
x2(s)= (7828707271/10000000000)exp(-s)-10000000001/10000000000;
x3(s)=-(166055512773/10000000000)exp(s)-(54800950897/5000000000)exp(-s)+140000000013/5000000000;

## While without procedures...

@Kitonum  The programs should work for any three points, and in the texts there is a check.
Creation of procedures in Maple yet not mastered by me.

## Circle in 3d...

Another way of constructing a circle by three points

CIRCLE_3_POINTS_geom3d_0.mw

## I'm a little surprised...

@vv
“I thought that you want to know how your surfaces really look (globally)”
You really thought so?

## Not a joke...

Then what is the point in Par3d, if the question was associated with this procedure? And what about the plane is not a joke.
(graph of  z-1/2 * exp (sin (x + 5/2 * y + z)) = 0.; continuous)

Merry Christmas!

## More examples...

Please show graphs of these functions:
(x^2+y^2-0.4)^2+(z+sin(x*y+z))^4-0.1=0.; (or can simply (x^2+y^2-2.)^2+z^2-1.=0.;)
x+y+z(+const)=0.;
If possible, and this function too:
z-0.5 * exp (sin (x + 2.5 * y + z)) = 0.;

## Rotated ellipsoid...

@vv
Is this the rotated ellipsoid?
x1^2+4.*x2^2+x3^2+x1*x2+x1*x3+0.1*x2*x3-2.=0.;

## Phonetics...

@vv
Lifetime work Anatoliy Vladimirovich on this subject no. Here is a Russian version in my presentation, where the second part describes the direct Draghilev method.
https://vk.com/doc242471809_437831729
As for phonetics, then Anatoliy Vladimirovich asked me to write his name in English Draghilev, which is almost exactly corresponds to the pronunciation of the Russian language.

## All right...

@vv
Yeah, right, but spell Draghilev. Draghilev method is not quite curve parameterization method in 3d, it was originally a method for solving systems of equations NxN, and it works much better than a continuation methods.
With regard to the parameterization of surfaces, it is the versatility for local application.
Although, let's try your "rotated ellipsoid"

## Unlikely...

@Carl Love

I think, that can be simplify the picture by increasing the step from the curves, but then the picture quality will be worse. And the text of the program, probably, can be optimized. How to simplify the algorithm, I do not know.
This, as well as the kinematics of linkages, based on solving underdetermined systems of equations. Many applied problems are related to the presence of free variables, and some of these problems when they clear to me, and when I have enough the degree of ownership of Maple, then the examples of solving these problems I am trying to show.

## break?...

@John Fredsted
And you did not try to use the break to control or stop the program in proper places? For example, I like this function (break) was very helpful.

## numpoints...

@Kitonum  It is unnecessary: "numpoints"

## Equidistant radius R = 0.1...

The numerical parameterization to calculate equidistant.
Surface:
(x1 ^ 2 + x2 ^ 2-0.4) ^ 2 + (x3 + sin (x1 * x2 + x3)) ^ 4-0.1 = 0;

x3-0.25*(sin(4*x1)+sin(3*x2+x3)+sin(2*x2))=0;

## Code...

Many thanks to all of you for your interest in the idea. The text  is almost the same, as was only to smooth I used polygonplot3d
Carl Love, I'm not sure that the creation of a common procedure would be an easy matter. It is necessary to take into account the direction of parameters on the surface, lengths of parameters , the choice of method for solving differential equations ... More need to connect the transformation that to deal with any kind of smooth surface.
But, again, for all  local graphs it will be much easier.

Maple 17:
EXAM_SQ_TORUS_POLYGON.mw

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