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1 vote
1 answer
72 views

Partitioning polygons into obtuse isosceles triangles

Ref: Partitioning polygons into acute isosceles triangles Partition of polygons into 'strongly acute' and 'strongly obtuse' triangles https://math.stackexchange.com/questions/1052063/...
Nandakumar R's user avatar
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1 vote
0 answers
76 views

Triangulation of polygons with all triangles having a common angle

Following Partition of polygons into 'strongly acute' and 'strongly obtuse' triangles, we record another triangulation question. Question: Given an n-vertex polygonal region ("n-...
Nandakumar R's user avatar
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6 votes
2 answers
210 views

Partition of polygons into 'strongly acute' and 'strongly obtuse' triangles

Definition: Let us refer to obtuse triangles with the largest angle strictly above a given cutoff value as 'strongly obtuse' - the definition is parametrized by the cutoff value. Likewise, strongly ...
Nandakumar R's user avatar
  • 5,837
1 vote
1 answer
534 views

Line segment-triangle intersection algorithm [closed]

currently in my project I'm using signed tetrahedron volume to check whether a line segment intersects a triangle. Initially I've found this approach in the great answer provided by professor O'Rourke:...
Mila Khan's user avatar
2 votes
4 answers
630 views

Show that the Minkowski sum of two triangles in 3D is the union of Minkowski sums of each triangle along the other's edges?

I'd like to show (or disprove) the claim that the Minkowski sum of two triangles with vertices in $\mathbb{R}^3$, $A+B$, is equal to the union of the unions of the Minkowski sums of $A$ along all ...
Alec Jacobson's user avatar
2 votes
3 answers
484 views

find the collision of a particle with a swept triangle.

Given there is triangle: V in 3D space that transforms over time t -> t1 to V1, and a static point P is somewhere in 3d space, how can I determine if P ever collides with V, and if so at what value of ...
Julian Mann's user avatar
7 votes
5 answers
1k views

How to compute the average distance till intersection within a triangle in $\mathbb{R}^2$?

You are given 3 points in $\mathbb{R}^2$; $A$, $B$, $C$ forming a triangle with area > 0. You pick an arbitrary point inside $ABC$ and an arbitrary direction. After some distance $d$, you will ...
user2814's user avatar
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