Questions tagged [geometry]
Questions on the application of Mathematica to geometric problems. You might also consider adding the [graphics] tag, if appropriate.
857
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Intersection point of two lines given starting points and ending points of both lines
I'm creating a program which requires me to get intersection point of two lines. I have tried using different formulas but none of them works perfectly for me. Following is one example which I found ...
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4
votes
3
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299
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Unify Polyhedrons into a single Polyhedron
Consider these two simple Polyhedrons which share a sub-face:
...
- 72.7k
2
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3
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386
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Shortcut of finding a tangent line and tangent point to a curve that's explicitly or implicitly defined
Any shortcut command of finding a tangent line and tangent point to a curve that's explicitly or implicitly defined? The focus is on implicit curves.
An implicit curve could be sth like $(x/exp(y)-1)^...
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2
votes
2
answers
327
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How do you calculate all the common tangents given two fixed circles and draw an image?
The two fixed circle equations given are known to be:
x^2 + y^2 == 1
(x - 3)^2 + (y - 4)^2 == 16
By calculating that they have three common tangents
...
- 72.7k
3
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1
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104
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0
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2
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168
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Finding the acute angle between two arbitrary lines
Given two arbitrary lines using primitives such as Line[{p1, p2}] in the plane, how can the acute angle between them be computed?
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- 483
3
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1
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Detecting lines in a 3D dataset
Premise
I have a 3D dataset of a system responding to different frequencies
https://pastebin.com/9MyQ6S74
(x: imposed frequency (f1)
y: response frequency
z: response amplitude)
I know that the system ...
- 1,396
5
votes
2
answers
224
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RegionMember Bug in 12.2?
Bug introduced in 12.2.0 or earlier. Fixed in 13.0.0 or earlier.
There appears to be an issue with RegionMember in Mathematica 12.2 when it comes to simple polygons and points.
...
- 15.3k
8
votes
5
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832
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Create a regular polygon with n vertices given two points
I want to create a regular polygon from the initial two points $A$, $B$ and number of vertices $n$,
regularPolygon[{0, 0}, {1, 0}, 3] gives ...
- 72.7k
3
votes
2
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148
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Is there a buit-in way to get a surface patch of a sphere for Graphics3D?
Mathematica 12.0 for Windows.
Is there a buit-in way to get a surface patch of a sphere for Graphics3D?
In this Graphics3D output, the sphere is only there for backing, and I only need (and want) part ...
- 1,457
6
votes
3
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Annular cylinder with varying dimensions
Consider a figure looking like the annular cylinder, with the longitudinal size extended from $z = 1$ to $z = 10$, but with the transverse boundaries depending on the distance from the origin $z$: the ...
- 72.7k
1
vote
1
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The different solution compare to the book solution?
On a book I found an integral with its solution I'm trying to solve it as well in Mathematica 13.2.0 but They are very different?!!!! If anyone can help it out!(integral : Sqrt[(3 x)/(x + 2 d)] d/(x -...
- 158k
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112
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Obtain a graph from a set of vertices
I have been looking into constructing a polyhedron from the coordinates of its vertices as discussed in the question linked below.
Construct a polyhedron from the coordinates of its vertices and ...
- 15.1k
2
votes
0
answers
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Generalise ImageLines to Image3DPlanes?
Context
I am interested in detecting (multiple) planes in a cube.
Test case
Let me first define a test case:
...
- 22.9k
5
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2
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222
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1
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1
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112
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Define a function on a MeshRegion
This looks like a simple question with the answer to be easily found, but unfortunately I could not find it either on the web or in the documentation browser.
Let us assume we have a MeshRegion ...
- 171
7
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4
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Numerically determining the minimum/maximum distance between two ellipses
The smaller ellipse is contained within the larger one.
By 'minimum distance', I mean the distance that minimises;
Sqrt[(y1 - y2)^2 + (x1 - x2)^2]
By maximum, I ...
- 71
2
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2
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200
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Region between finite lines or extracting a finite tesselation
EDIT2 the answers here (How to compute intersections of circles on a lattice) seem like they could help or solve the problem.
EDIT: I saw this question about finding regions between lines before I ...
- 19.1k
5
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2
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172
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Strange behaviour in GeometricTransformation
Bug introduced in 13.0
**Bug is fixed in Version 13.1 **
I came across the following strange behaviour with the GeometricTransformation function.
...
- 4,023
-1
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1
answer
206
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Tangents of 2 circles [duplicate]
I am trying to write a function, tanCircles[], that finds the common tangents to two given circles (one not inside the other). The function's parameters are two list, each containing the x and y ...
- 51.7k
28
votes
3
answers
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How to simulate the true reflective movement of a particle bouncing around in an ellipse?
Please help me to simulate the movement of a particle inside a region with elliptical walls such that particle is reflected from the walls and continues to move.
A friend was able write code to ...
- 72.7k
2
votes
1
answer
89
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Inaccuracy in triangles computation
The below link on MSE was a question assuming a second solution was obtained on Mathematica by second method. Appears to be a question of accuracy.
Big Side of Triangle
Given are three side lengths $ (...
- 72.7k
2
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2
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390
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I need to find the obtuse angle between the following two lines
I need to find the obtuse angle between two lines but I am not sure how to code it.
my two angles are 𝑥+√3𝑦=1 and (1−√3)𝑥+(1+√3)𝑦=8
I already did the calculations but im just not sure how ...
- 72.7k
5
votes
2
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528
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How could I generate random convex polygons of area 1?
How could you random convex polygons where the points of the graph
$A(x_1,y_1) , B(x_2,y_2), ... $
come out, hopefully in rational format (a/b) in such a way that the total area of the polygon is ...
- 9,808
1
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2
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112
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How to randomly insert a region inside another region like RandomPoint?
With RandomPoint one can find a random point inside of a region. I would like to instead obtain a region randomly placed inside another region. One possibility ...
- 5,857
3
votes
2
answers
264
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Confusion surrounding Mesh for a complicated function
I have two different setting with the command Mesh, one is at All and the other one is at 2000. I just don't have the math to understand what I am seeing.
...
- 32.5k
3
votes
3
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422
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How to find the angle of a rotation matrix
I know there is post about finding angles of rotation matrix, but all of them required more than a rotation matrix, I want to know that If I have a matrix ...
- 26.7k
1
vote
0
answers
64
views
How to get the closest point from the known point to a fractal tree？
Given a known point, how to analytically find the nearest point from the point to the fractal tree?
The fractal tree code:
...
- 11
2
votes
1
answer
91
views
How to create a line with a label centered above it?
Can anyone help me create a line with a label shown in the picture below? The line is discontinuous near the middle to accomodate the label. The label is placed on top to avoid the problem when the ...
- 53.7k
7
votes
3
answers
517
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Track chord movement
The point $P$ on the circle and the point $F$ inside the circle, perpendicular bisector of line $PF$ intersects the circle at two points $A, B$, the envelope of $AB$ is an ellipse.
I use the following ...
- 26.3k
2
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0
answers
46
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How to make an efficient SimplyConnectedQ (check for abscence of holes)?
I would like to find an efficient way to detect whether a region has a hole regardless of how many it has. This question (Separate boundaries of multiply connected region) shows some methods but it ...
- 5,857
3
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1
answer
254
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Enlarge polygon by fixed edge distance [duplicate]
I wish to create a larger polygon from a smaller one through orthogonally translating each edge by a fixed distance. RegionResize with a bounding box given by ...
- 72.7k
1
vote
1
answer
62
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Circumference of an ImplicitRegion
I define an ellipse by using an ImplicitRegion:
R = ImplicitRegion[4 z^2 + r^2 == 10, {z, r}]
I would like to get the perimeter of this ellipse. I was hoping to ...
- 72.7k
5
votes
1
answer
187
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Sort symbols or characters by image complexity
As an example, I would like to sort the following characters by some sort of complexity measure:
...
- 5,857
1
vote
1
answer
71
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Calculate the area using parametric plot
i would like to ask a question
if we have some parametric plot and it will be a shape, can we use "area" function to calculate that shape?
Here is the simple program
...
- 72.7k
0
votes
1
answer
73
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Region Plot using Point data [closed]
so far I use a listplot to create a geometry from a data point. to use the are feature, it requires using the region. anyone know how to make a geometry from point data using region plot?
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- 157
28
votes
12
answers
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how to get $n$ equidistributed points on the unit sphere
We can get $n$ equidistributed points in the unit circle using CirclePoints. But how do you get $n$ equidistributed points on the unit sphere(surface of a ball)? ...
- 221
6
votes
5
answers
2k
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Distance between two line segments in 3-space
I need to compute the distance between two line segments in a project. After googling, I found this algorithm and used it to implement a Mathematica version:
...
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1
answer
158
views
5
votes
1
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394
views
Obtaining the curve parallel to the function a/(x^2+b)
I would like to obtain a curve that is parallel to the function:
y(x) = -a/(x^2 + b)
I have tried to calculate the said curve by solving parametric equations, but ...
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2
votes
0
answers
175
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How to convert a lat long Earth position at a given time to J2000 inertial coordinate system coordinates
Given a Date object (i.e. a moment in time) and an Earth relative position (lat long and altitude), how does one derive the position expressed in J2000 celestial inertial coordinates?
Thanks!
Kerry ...
2
votes
4
answers
225
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Counting number of points in fluctuating lines that fall within a circle
I have a list of points pts that fluctuate around some mean line. pts is pre-sorted by the projection of the points onto this ...
- 19.1k
3
votes
2
answers
167
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Plotting a $3$-dimensional convex shape consisting of portions of six spheres
How can we plot a convex shape $C$ in the $3$-dimensional Euclidean space, whose boundary $\partial C$ is formed by portions of six different spheres, one portion per sphere? The radius of each sphere ...
- 34k
-1
votes
1
answer
147
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Distance of a point from a line using multiplicative distance [closed]
How can we determine the multiplicative distance (http://link.springer.com/article/10.1007/s10115-014-0813-4#page-1) of a point (x0,y0) from a line (ax+by+c=0)?
Let X = (x_1, x_2 ..., x_m) be a ...
- 11
0
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1
answer
82
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Graphing and calculating the volume using mathematica (or other)
I posted the following in MSE: (See Here)
Consider two cylinders Cs (solid) and Ch (hollow):
Cylinder Cs has a radius rs, and has the points (x1,y1,z1) and (x2,y2,z2) as the centers of its bases.
...
- 5,187
3
votes
5
answers
998
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Calculating length of curve based on data points?
I had around $1000$ data points $(x,y,z)$ and when I plot them they seem to lie on a closed curve. I carefully checked the data points and the points do not repeat rather they are somewhat close to ...
- 199
2
votes
2
answers
394
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How can I make points equally spaced along any line?
What I am looking for is something like the output of this code:
...
- 72.7k
1
vote
4
answers
266
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A square with different centers and sides of different lengths
As you can see the bottom square is in the ${((0,2),(0,2))}$ range
The center of the square is indeterminate
The length of a square is indeterminate
The length of the square is indeterminate, and $1/...
6
votes
2
answers
211
views
Systematically generate Corner and Centered polygonal diagrams?
A polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. Namely, it is "a type of figurate number which is a generalization of triangular, square, ...
4
votes
2
answers
188
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How to calculate different combinations of back and dotted perimeter
I have this code that generates the image below, my question is how to calculate the area and perimeter of the first figure and all the variations of it considering a side of square "L" or ...
- 15.5k