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- ArticleJanuary 1988
Arrangements of lines in 3-space: a data structure with applications
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 371–380https://doi.org/10.1145/73393.73431Let an arrangement of blue lines in 3-space be fixed, and imagine a movable red line entangled in the arrangement. We show an Ο(n4α(n)) algorithm for building a data structure that permits enumeration of mutually inaccessible classes of such red lines, ...
- ArticleJanuary 1988
Skewed projections with an application to line stabbing in R3
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 362–370https://doi.org/10.1145/73393.73430A new geometrical transform, skewed-projection, is introduced. This transform is applied to design a new algorithm for a common transversal problem for families of polyhedra in R3. The time and space analysis, using Davenport-Schinzel sequences, is ...
- ArticleJanuary 1988
An efficient output-sensitive hidden surface removal algorithm and its parallelization
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 193–200https://doi.org/10.1145/73393.73413In this paper we present an algorithm for hidden surface removal for a class of polyhedral surfaces which have a property that they can be ordered relatively quickly like the terrain maps. A distinguishing feature of this algorithm is that its running ...
- ArticleJanuary 1988
Hidden surface removal for rectangles
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 183–192https://doi.org/10.1145/73393.73412A simple but important special case of the hidden surface removal problem is one in which the scene consists of n rectangles with sides parallel to the x and y-axes, with viewpoint at z = ∞ (that is, an orthographic projection). This special case has ...
- ArticleJanuary 1988
The design of LINETOOL, a geometric editor
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 83–92https://doi.org/10.1145/73393.73403We describe the design of LINETOOL, a geometric editor. Researchers in the areas of computational geometry, robotics and algebraic computation need a graphical editor for composing geometric objects which does more than simply turn pixels on and off on ...
- ArticleJanuary 1988
Implicitly representing arrangements of lines or segments
SCG '88: Proceedings of the fourth annual symposium on Computational geometryPages 56–69https://doi.org/10.1145/73393.73400An arrangement of n lines (or line segments) in the plane is the partition of the plane defined by these objects. Such an arrangement consists of Ο(n2) regions, called faces. In this paper we study the problem of calculating and storing arrangements ...