Problem 1446. Minimum Distance Point to Segment

Created by Richard Zapor

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This Challenge is to determine the minimum distance from a 2-D line segment defined by two points to a point.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The point is (px,py) and the segment is [(vx,vy) to (wx,wy)].</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Input are the three defining points and the output is distance.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Input (px py vx vy wx wy):</w:t></w:r><w:r><w:t> 1 1 0 3 3 0</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Output distance:</w:t></w:r><w:r><w:t> .7071</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Point is beyond perpendicular to segment.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Input (px py vx vy wx wy):</w:t></w:r><w:r><w:t> 4 3 -100 0 0 0</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Output distance:</w:t></w:r><w:r><w:t> 5</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Follow Up Challenges:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>1)</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/1452-minimum-distance-between-two-n-sided-polygons\"><w:r><w:t>Minimum distance between non-contiguous N-sided polygons</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>2)</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/1457-usc-spring-2013-acm-walking-on-thin-ice\"><w:r><w:t>USC Spring 2013 ACM: Walking on Thin Ice</w:t></w:r></w:hyperlink></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

253 Solutions
49 Solvers

Last Solution submitted on May 04, 2021

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

David Gines on 14 Jun 2013

Is a numerical approximation allowed, or should one use the geometric formulas?

Solution Comments

Solution 261431

1 Comment

1 Comment

Richard Zapor on 15 Jun 2013

Solid calculus dot product exact geometric solution.

Solution 234574

1 Comment

1 Comment

Richard Zapor on 23 Apr 2013

Crushed by Tim, once again.

Problem Recent Solvers49

Problem Tags

distance geometry line

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 1446. Minimum Distance Point to Segment

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers49

Suggested Problems

More from this Author255

Problem Tags

Community Treasure Hunt

Problem 1446. Minimum Distance Point to Segment

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers49

Suggested Problems

More from this Author255

Problem Tags

Community Treasure Hunt

Players