Common Tangents to Four Unit Balls in R3
نویسندگان
چکیده
منابع مشابه
An Enumerative Geometry Framework for Algorithmic Line Problems in $\mathbb R^3$
We investigate the enumerative geometry aspects of algorithmic line problems when the admissible bodies are balls or polytopes. For this purpose, we study the common tangent lines/transversals to k balls of arbitrary radii and 4− k lines in R3. In particular, we compute tight upper bounds for the maximum number of real common tangents/transversals in these cases. Our results extend the results ...
متن کاملCommon Tangents to Four Unit Balls in R
We answer a question of David Larman, by proving the following result. Any four unit balls in 3-dimensional space, whose centers are not collinear, have at most twelve common tangent lines. This bound is tight.
متن کاملCommon Tangents to Spheres in R3
We prove that four spheres in R3 have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.
متن کاملLines Tangent to Four Triangles in Three-Dimensional Space
We investigate the lines tangent to four triangles in R3. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.
متن کاملLines Avoiding Unit Balls in Three Dimensions
Let B be a set of n unit balls in R3. We show that the combinatorial complexity of the space of lines in R3 that avoid all the balls of B is O(n3+ε), for any ε > 0. This result has connections to problems in visibility, ray shooting, motion planning, and geometric optimization.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 26 شماره
صفحات -
تاریخ انتشار 2001