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Results tagged with convex-geometry
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user 38468
A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
3
votes
Show that the Minkowski sum of two triangles in 3D is the union of Minkowski sums of each tr...
Let $a_i$ and $b_j$ be the vertices of the triangles. For a given point $p$ in $A+B$ the space of solutions $(\alpha_1,\ldots,\beta_3)$ to
$$
p = \sum_i \alpha_i a_i + \sum_j \beta_j b_j, ~\sum_i \al …
- 5,186
2
votes
polynomial expression for counting number of integral points of a set
Let's see what happens in dim 2. You have $conv((0,0),(ra_1+sb_1,0),(0,ra_2+sb_2))$. The number of points in the closed triandle $(0,0),(A,0),(0,B)$ is $(A+1)(B+1)/2$ plus half the number of points on …
- 5,186
1
vote
Accepted
A question about rational convex cone
Counterexample: lattice is $\mathbb Z^2$, $S = \{(1,0),(1,1),(1,3)\}$, $v=(1,2)$.
- 5,186