All Questions
94
questions
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53
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Find the co-ordinates of a 3D triangle $ABC$ given 2 unit vectors, a side and a property
There is a triangle $ABC$ in 3D space. I am given the following:
$\vec{u}_{AC}:$ The unit vector along the direction of $AC$.
$\vec{u}_{BC}:$ The unit vector along the direction of $BC$.
point $A$ ...
- 105
1
vote
0
answers
40
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Fibonacci or Lucas sequence and triangles
I'm not a mathematician by any stretch. I do not have any formulas to produce here. I am just wondering if you find this interesting as well and any opinion you have on this observation.
I was ...
- 11
2
votes
1
answer
60
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Find tetrahedron triangles' angles from dihedral angles.
Finding dihedral angles between tetrahedron faces from triangles' angles at the tip has been answered in:
Dihedral angles between tetrahedron faces from triangles' angles at the tip
My questions ...
- 31
2
votes
1
answer
71
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If the triangle is revolved about its any side such that the volume of solid so obtained is $128\pi$, find the radius of the circle.
A triangle with maximum area is cut from a circle. If the triangle is revolved about its any side such that the volume of solid so obtained is $128\pi$ cm$^3$, then find the radius of the circle.
My ...
- 8,338
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0
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34
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Formula name to scatter 3D points in a triangle.
I was looking for how to scatter a 3D point into a triangle surface and I found the answer in this post here:
How to sample points on a triangle surface in 3D?
Basically, the formula that I was ...
-1
votes
1
answer
1k
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Orientation of a triangle's vertices in 3D space: Clockwise or counter clockwise?
Consider the following theoretical framework I’ve come up so far from bits and tips, mainly from Wikipedia and Orientation of three points in 3D space :
Given ${E}$, an Euclidean space $\Bbb R^3$ with ...
1
vote
1
answer
55
views
orientation difference between two triangles in 3D space
Lets there be 2 sets of 3 points in 3D space, representing 2 congruent isosceles triangles. The apexes of both triangles are located at the point (0,0,0). How do I calculate the difference between the ...
0
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1
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41
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geometry what structure is derived from half a parallelepiped structure
the question comes from vector and determinants.
we all know that two 2D vectors v, and w, is a parallelogram. and half this is an triangle.
they can be found by the determinant.
i wanted to extend it ...
0
votes
1
answer
113
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Test if point in 3D is above triangle using vertex normals
Please, my problem is very close to Find a point on triangle and interpolated triangle normal which points to specific point in 3D, but I do not need to find analytical/numerical solution. I rather ...
1
vote
1
answer
203
views
Angle between two "directed" triangles in 3D between 0 an 2 pi
I have two triangles in a 3D space, each one defined by three vectors. The two trianlges share an edge.
Beside that I have a normalized vector for each triangle (perpendicular on it) defining a "...
- 131
1
vote
0
answers
135
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Does $c^2 \leq a^2 + b^2$ hold for right triangles on the sphere?
I was hoping for a proof of something which appears to be intuitive to me, but which I can't prove.
Let $a, b$ & $c$ be lengths of the sides of a triangle. We know that on a plane, $c^2 = a^2 + b^...
- 11
1
vote
1
answer
718
views
Sum of "angles" of a 3D tetrahedron
We know that the sum of angles of a triangle equals the straight angle (180 degrees).
Can we convert a 2D theorem to 3D?
e. g. We can generalize the triangle to a tetrahedron, angles of the triangle ...
- 65
3
votes
1
answer
2k
views
Volume of a triangular prism with 2 different bases
How do I arrive at a formula to calculate the volume of the following 3D shape? Does this shape have a proper name?
It kind of looks like an irregular triangular prism with 2 similar triangles as ...
- 133
0
votes
1
answer
207
views
Find a point on triangle and interpolated triangle normal which points to specific point in 3D
Suppose i have triangle in 3d with vertices $v1, v2, v3 \in R^3$. Each triangle vertex has associated normal vector $ n1, n2, n3 \in R^3, ||n_i|| = 1$.
In computer graphics such vectors sometimes ...
- 277
0
votes
0
answers
46
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Angle optimisation problem in 3 dimensions.
I came across this question in test.
Given $A(0,0,1), B(2,1,2)$ be two points in 3-D space also P($\alpha ,\beta$) ($\alpha>0 ,\beta>0$) be a point on the xy-plane
such that $\angle APB$ is ...
- 165