Re: How easy is it to solve geometry problems in Mathematica?
- To: mathgroup at smc.vnet.net
- Subject: [mg9725] Re: How easy is it to solve geometry problems in Mathematica?
- From: "Paul R. Wellin" <wellin>
- Date: Tue, 25 Nov 1997 00:06:21 -0500
- Organization: Wolfram Research
- Sender: owner-wri-mathgroup at wolfram.com
jmthomas wrote:
>
> Computational geometry IS a big machine! If you need to find a line
> tangent to Curve1 which is an ellipse and Curve2 which is another
> ellipse, you can write a standard solution in let's say an hour.
> If you need to write a function taking any two curves as arguments, you
> are expecting too much.
> Start with an easy two dim problem: intersection of two lines: define
> your objects: a line is either a linear relation ax+by+c==0, or a
> pair of points p1={x1,y1} and p2={x2,y2}, or a point and a vector.
> When your procedure is written, and checked, you will have elements to
> your questions.
Take a look at Tom Wickham-Jones' book "Mathematica Graphics" in which
there are discussions and functions defined for doing lots of
interesting things in 2D geometry (this list below does not include all
the computational geometry included in TWJ's book), including:
- computing dot and cross products
- visualizing normal vectors
- discussions of explicit vs. implicit line representations - geometric
translations, rotations, shears - affine transformations
- computing the intersection of two lines - tests for determining if a
point is on a line - computing the minimum distance from a point to a
line - determining which side of a line a point is on - determining
whether a point is inside or outside a given triangle - perimeter and
area of triangles
- computing circles inscribed in and circumscribed about triangles
(Analagous problems in 3D are also presented.) What you will find
interesting is the simplicity of each of the above programs. These
should help you to define functions for your own particular needs.
Paul R. Wellin
Corporate and Academic Affairs
Wolfram Research, Inc.
> ----------------------------------------------- Jean-Marie THOMAS
> Conseil et Audit en Ingnierie de Calcul jmthomas at cybercable.tm.fr
> www.cybercable.tm.fr/~jmthomas
>
> -----Original Message-----
> From: Maggie Eusebio Schock [SMTP:cjs19 at cornell.edu] To:
To: mathgroup at smc.vnet.net
> mathgroup at smc.vnet.net
> Sent: Thursday, November 13, 1997 7:41 AM To: mathgroup at smc.vnet.net
> Subject: [mg9725] [mg9574] How easy is it to solve geometry problems in
> Mathematica?
>
> I would like to solve 2D geometry problems of this nature:
>
> Find a line tangent to two curves (curves such as ellipse, circle,
> circular arc, elliptical arc or splines)
>
> Find the intersection point between to curves.
>
> Is it fairly easy to solve these in Mathematica? I am considering
> purchasing Mathematica and would like to have your inputs.
>
> Thanks in advance.