Questions tagged [geometry]

Questions on the application of Mathematica to geometric problems. You might also consider adding the [graphics] tag, if appropriate.

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Finding 3d circle center

Num calcn for Tria Center Can someone please help in finding an analytic expression for the center of a circle through 3 given points by modifying ( Solve in place of NSolve ) a conventional numerical ...
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2 votes
1 answer
74 views

Get the correct branch form Solve

I am reproducing the derivation in this article (exploration of a family of circles centered on an ellipse). I only need the outer curve, the results obtained from Mathematica are more complicated ...
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2 votes
1 answer
70 views

Strange behaviour in GeometricTransformation

I came across the following strange behaviour with the GeometricTransformation function. ...
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  • 3,524
0 votes
1 answer
58 views

How to find PlanarAngle[] across periodic boundaries?

Suppose we have a collection of points selected as being within a certain radius (0.1) of myCenterPoint: ...
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  • 1,303
13 votes
5 answers
807 views

Divide a geometric region by (many) lines

Given a shape (e.g., a rectangle, a circle, etc.), how to divide it by $n$ randomly chosen lines. It is trivial to plot those lines (see figure below), using code like ...
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1 vote
0 answers
78 views

How to find the center of gravity of fibers in image

I am trying to find the centers of gravity of my particles in a SEM image. I binarized the image (img) and with the input and help of previous suggestions on that topic (Creating graph out of ...
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4 votes
3 answers
142 views

Hemisphere volume plot

I am trying to show an animation of the hemisphere volume. I tried to start with some radius and rotate it, to get an area of a circle. Then, I will stack up the circle in z-axis to make a hemisphere. ...
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  • 85
5 votes
1 answer
140 views

How to combine several surfaces into a solid and compute its volume?

plot1 is taken from the BSplineSurface document. I add two Disk ...
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6 votes
2 answers
458 views

How to quickly test if two regions intercept?

If I randomly generated two cylinders, how do I test if they intercept? For example: ...
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  • 123
3 votes
2 answers
159 views

How to draw two tangentlines to the circle in the complex plane

From the origin(0,0) of the complex plane, draw two tangent lines to the circle (see plot (p1)). The absolute value of a complex number is a vector from origin to complex number in complex plane. <...
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1 answer
101 views

How can I get the volume enclosed by two orthogonal cylindrical surfaces?

With the following code, I can only get the results when the radius of the ball and the half apex angle of the cone are specific values. ...
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5 votes
2 answers
364 views

How can I get the volume enclosed by two orthogonal cylindrical surfaces (Radius is a variable, not a specific value)?

I can get the volume enclosed by two orthogonal cylindrical surfaces when the radius of the bottom circle of the cylinder is a specific value (for example, r1=r2=2): ...
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0 answers
151 views

The Nagel point revisited

Let $i$ be the incenter of the triangle $\triangle abc$, and $n$ be the Nagel point of this triangle (see Wiki ). Let also $h_3$ and $h_2$ be the orthocenters of the triangles $\triangle iab$ and $\...
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4 votes
2 answers
130 views

ParametricRegion is not showing complete region

I am trying to plot a region using the following code ...
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4 votes
3 answers
220 views

How to construct the Nagel point of a triangle with GeometricScene?

Let us consider the Nagel point of a triangle. According to this article,"There exists an easy construction of the Nagel point. Starting from each vertex of a triangle, it suffices to carry twice ...
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4 votes
0 answers
84 views

Why am I losing photons in a window?

I'm trying to model a window. For some distribution of light rays hitting the window, I'd like to determine the output angles, and the number of photons which are reflected or transmitted. I'd like ...
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  • 3,842
0 votes
1 answer
109 views

How to simplify the equation of this 3D-straight line?

Find the equation of the line passing through the point (2,1,3) and perpendicular to the line (x + 1)/3 == (y - 1)/2 == z/-1 and having an intersection point. ...
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2 votes
2 answers
81 views

How to deduce cosine theorem with vector?

I want to prove the cosine theorem of triangles with vectors under the following assumptions: ...
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0 votes
0 answers
69 views

Calculate the "intersection" for the given case?

Consider the following task: There are two cross-sections: the first one is located in the $yz$ plane (the case 1), and the second one is in the $xy$ plane (the case 2). In the spherical coordinate ...
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5 votes
5 answers
411 views

Normal equation of plane through a point and line

I need to find the normal vector of the form Ax+By+C=0 of the plane that includes the point (6.82,1,5.56) and the line (7.82,6.82,6.56) +t(6,12,-6), with A=1. Of course, this is easy to do by hand, ...
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  • 127
14 votes
4 answers
568 views

How to plot Morley triangle by Synthetic Geometry method?

As the Wiki The three points of intersection of the adjacent angle trisectors form an equilateral triangle, called the Morley triangle So I write this code: ...
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0 votes
0 answers
59 views

RegionCentroid giving different result on Polygon and ConvexHullMesh

I have the following 5 vertices: ...
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0 votes
0 answers
66 views

How to create an animating torus using mathematica or python? [duplicate]

I want to create this animating torus using mathematica or python. If anyone knows how to make this please try to explain the steps. Thank you zo much.
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12 votes
2 answers
461 views

How to separate the regions enclosed by curves

There are three arbitrary curves that defined by three implicit functions. How to separate the 12 regions(one of them is the outside infinite region) Although we can use image methods to distinguish ...
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6 votes
3 answers
327 views

How can I change the triangles vertices points to other geometric figures?

I want to convert the triangle's vertices points into hexagons like in the image above, where all the distances are the same, a=1 for example. I've tried to use TranslationTransform ...
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2 votes
0 answers
82 views

How to write on a surface?

How do I include text on a curved surface? For example, and as a starting point, how can I reproduce the following image I've seen some examples where people geometrically described letters to do ...
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  • 4,138
2 votes
1 answer
103 views

GeometricScene revisited [closed]

Studying a new command GeometricScene, I try ...
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  • 16.6k
1 vote
1 answer
140 views

Why the difference in GeometricScenes?

Studying a new GeometricScene command, I try ...
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  • 16.6k
1 vote
2 answers
104 views

why does the MomentOfInertia behave differently for ConvexHullMesh and ConvexHullRegion

I have a list of points of a convex polyhedron for which I need to compute the eigenvectors of the Moment of Inertia matrix. But, it seems like the built-in ...
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  • 8,528
5 votes
0 answers
84 views

CirclePoints and CircleThrough

$Version 12.2.0 for Microsoft Windows (64-bit) (December 12, 2020) For points (located on a unit circle), ...
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  • 14.6k
5 votes
3 answers
198 views

Is there an inverse function of LineScaledCoordinate?

I know a useful function LineScaledCoordinate through animate-point-going-around-a-triangle, so does it have an inverse function? ...
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  • 6,510
8 votes
2 answers
552 views

Make polygon rolling along a line smoothly

I'm making an animation of a polygon rolling along the X-axis, the labels should keep their orientation and float is not allowed. Now lack of transitional status, is there an simpler way to add a ...
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  • 6,510
2 votes
3 answers
175 views

How to find an equation of this 3D-straight line?

For didactic purposes I'd like to find an equation of the 3D-straight line passing through the origin and intersecting both 3D-straight lines $\{x-y+z-2=0, x-2 y+3 z-8=0\}$ and $\{y - z + 1 = 0 , x + ...
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  • 16.6k
1 vote
0 answers
108 views

How to find quadrilateral with maximum area?

Let the lengths of the sides of a quadrilateral equal a,b,c,d. What is the maximum area of such quadrilaterals? Wiki says that the quadrilateral with its maximum ...
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  • 16.6k
2 votes
3 answers
253 views

Finding Ellipse Axes

Consider the following ellipse, generated by the bounding region of the following points ...
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  • 4,138
5 votes
1 answer
117 views

Avoiding Concave Polygons

In a vertex model, vertices in a lattice are modelled by a set of ODEs. A T1 transition is the following: when a certain edge becomes small enough (given a threshold), two cells stop being connected, ...
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  • 4,138
1 vote
4 answers
169 views

Equations for a perfect cylinder intersecting a thin plate with a circular cutout

Given a perfect cylinder of diameter D standing vertically and of an arbitrary length, and a thin flat plate with a circular cutout which is a slightly larger diameter than D, and they are ...
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5 votes
2 answers
329 views

How to make a dynamic plot of a holed circle using "Manipulate"

I would like to make a dynamic circle with the inner radius ($R_a(t)$) moving to $R_b$ like the image below. I had difficulty using Manipulate and leaving the intersections colored as in the image. ...
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  • 53
1 vote
1 answer
141 views

How to use VectorAngle[] in AnglePath3D[]?

Suppose I have a specific angle that I calculate from two vectors, in 3D: ...
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  • 1,303
4 votes
2 answers
478 views

3d printing flat pattern

Four copies of a flat region defined below ( length AH = 10 mm and prism Thickness= 2 mm typically) is to be 3d printed so that edges LM,KI coincide. Writing ...
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  • 2,806
12 votes
1 answer
270 views

Rectangle packing, fixed sizes

I have rectangles of a given size to fit into a larger rectangle of a fixed size, with a specified gap between the packed rectangles. I would like to write some code that optimises the number of ...
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  • 7,759
-2 votes
1 answer
135 views

How Can I Visualize a PDE Boundary Condition? [closed]

I want to use Mathematica to visualize boundary/initial conditions for PDEs in 3-dimensional space. This was sparked by the initial comment in this question, which attempts to solve the PDE $$\...
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  • 129
0 votes
1 answer
58 views

Quarter circle surface opening outward

I have a Graphics3D issue, I have a cylinder within a cylinder. I want to generate a surface from a quarter circle, but the quarter circle should be "curving ...
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5 votes
1 answer
146 views

Problem with RegionMember

I think there is potentially a bug in RegionMember function, particularly in the RegionMember[reg] form. Can you evaluate the ...
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  • 8,528
12 votes
8 answers
1k views

Checking if two line segments intersect

What is the fastest way of checking whether two line segments of the form Line[{p1,p2}] intersect at a point? I don't need to know what the point of intersection is,...
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  • 4,138
0 votes
0 answers
76 views

Plot is fast, solve is slow - what optimizations can be made?

I'm trying to solve a 3D geometric problem in terms of 3 variables (rotational angles), and I think the end is finally in sight - quite literally, I can see on a 3D plot where my solution exists. ...
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  • 101
11 votes
3 answers
367 views

Color regions defined by many lines

Consider the following code: ...
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  • 912
5 votes
1 answer
172 views

Rotation/Viewing options for 3D plots

Preamble In this post from several years ago: , it has been suggested that a "Globe" method is available for RotationControl. ...
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  • 14.6k
3 votes
3 answers
352 views

How to draw arrows of certain length from a point, at a certain angle?

What's the specification to draw arrows of a certain length (from a reference point), at a given angle? Say, I want to draw an arrow of length 1 at 0 degrees, and one of length 0.5 at 90 degrees, each ...
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  • 1,303
4 votes
1 answer
224 views

Project geomap onto band of sphere

A band surrounding a sphere could be plotted using the ParametricPlot3D function: ...
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