Problem 2083. Independent direction vectors of a plane

Created by Marcel

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; "><div style="font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379px 8px; transform-origin: 379px 8px; unicode-bidi: normal; "><span style="">Given the equation of a plan of the form ax+by+cz=d, return 2 independent direction vectors which could e.g. be used to determine a parametric equation.</span></span></div></div></div>

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69 Solutions
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Last Solution submitted on Aug 11, 2023

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Tim on 31 Dec 2013

For the vectors to be independent, the test suite should have assert(dot(v1,v2)==0).

Alfonso Nieto-Castanon on 4 Feb 2014

instead of assert(dot(v1,v2)~=0) ...

J-G van der Toorn on 6 Feb 2014

I agree. First, I did not succeed for that reason.

J-G van der Toorn on 6 Feb 2014

I am curious about the 26-node solution.

Christian Schröder on 26 Feb 2023

This is unfortunately suffering from many issues.

1. Many cases (planes parallel to one or two axes) aren't covered in the test suite.
2. Exact equality tests are used for floating-point comparisons, which can lead to spurious failures.
3. assert(dot(v1, v2) ~= 0) doesn't make sense, as remarked.
4. Neither would assert(dot(v1, v2) == 0), however, since the direction vectors are required to be (linearly) independent, not orthogonal.

Dyuman Joshi on 26 Feb 2023

Christian, I think the assertion dot(v1,v2)~=0 is placed to ensure that the two vectors are not parallel and therefore are independent.

I have modified the assert conditions and added some test cases to reflect planes parallel to axis/axes.

Christian Schröder on 27 Feb 2023

Thank you, Dyuman!

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Problem 2083. Independent direction vectors of a plane

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Problem 2083. Independent direction vectors of a plane

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