What kind of geometric intersection

Should be able to do with integer arithmetic only. Given N line segments, find all intersections. Perhaps omit this since it involves floating point or rational arithmetic and dealing with alot of degenerate cases.

For simplicity, we assume no horizontal segments. Also, when segments intersect, it is only at a single point, and at most two segments intersect at a given point.

Still susceptible to roundoff errors. Segments crossing sweepline at nearly same point, almost vertical segments, a segment with one endpoint almost on another segment. Perhaps use exact rational arithmetic??? Overlapping intervals. Max bandwidth. VLSI design. Simple idea that almost works: decompose 2D intervals into hv line segments, and check for proper line segment intersections.

This doesn't quite work if we detect improper intersections in the hv intersection subroutine. More seriously, this approach fails to detect nested cases, where one 2D interval is entirely inside another. Sweep line algorithm. Run a sweep-line from left to right. Maintain an interval search tree of intervals of the active y-intervals which intersect the sweep line. Left-endpoint of a 2D interval: find all intersections with y-interval in interval search tree; then add the y-interval to the interval search tree.

Right-endpoint of a 2D interval: delete the 2D interval. Program VLSI. It uses intervals with integer-valued endpoints: Interval1D. The interval search tree IntervalST. Degeneracies: assumes no two y-intervals are identical. Rotating cube. Hidden line removal with linear algebra for rotations and translations.

Exercises Union of intervals. Given N intervals on the real line, determine the length of their union in O N log N time. For example the union of the four intervals [1, 3], [2, 4. Hint: sweep line sort by left and right endpoints.

All HV intersections. Find and report all HV line segment intersections. For simplicity Assume that no two segments share the same x or y coordinate.

Proper HV line intersection. Modify HVIntersection. Area of union of rectangles. Given a set of axis-aligned rectangular boxes, devise an O N log N algorithm to compute the area of their union. Hint: sweep a vertical line from left to right, maintaing the intersection of the rectangles and the sweep line in an interval search tree as in VLSI design. When the sweep line hits a vertical edge, update the interval search tree as in VLSI and also update the cumulative area swept so far.

When all the inputs are point feature classes, the Intersect tool can be used to determine which points are common to all input feature classes.

Intersect can be used with feature classes of different geometries. The default and highest allowable Output Type is the same as the feature class with the lowest dimension geometry. The graphic below illustrates the result of intersecting line and polygon feature classes with the Output Type parameter set to LINE.

The output line features are where a line from one of the input feature classes overlaps a polygon from the other input feature class. The output point features are where line endpoints touch at a point on the polygon boundary and where lines cross polygon boundaries.

No points are generated in the output where lines lie directly along polygon boundaries. The graphic below illustrates the result of intersecting point, line, and polygon feature classes. The output can only be a point feature class. Each point in the output will intersect at least one feature in each of the input feature classes. Feedback on this topic? Back to Top. Intersect does the following: Determines the spatial reference for processing.

Other solutions. View Full Material. Are collinear People also purchased. Standard Normal Distribution. In Exercises 17—36, assume that a ra The following plot shows the potential energy of two Cl atoms as a The iodi Exercises involve the method of acceptance sam Related chapters.

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