check points inside triangle or on edge with example

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Redwan Dan 2016-4-8

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https://ww2.mathworks.cn/matlabcentral/answers/277984-check-points-inside-triangle-or-on-edge-with-example

回答： Gary Bikini 2021-6-12

采纳的回答： Roger Stafford

Good evening everyone

function or coding for finding point is inside triangle or sub triangle or its on edges

thanks for involving your knowledge to be share to answer question

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Roger Stafford 2016-4-9

I've given the necessary expression as an "Answer" here. It doesn't seem like a very slow method to me.

Walter Roberson 2016-4-9

Redwan Dan comments to John D'Errico:

am not here to prove you any thing and the way your answer and close is not nice treat with me if you don't know just don't comment or close

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采纳的回答

Roger Stafford 2016-4-9

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https://ww2.mathworks.cn/matlabcentral/answers/277984-check-points-inside-triangle-or-on-edge-with-example#answer_217122

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Suppose P1 = [x1,y1], P2 = [x2,y2], and P3 = [x3,y3] are row vectors giving the coordinates of the three vertices of a triangle, and P = [x,y] is a row vector for the coordinates of a point P. To determine whether P lies inside the triangle P1P2P3 do this:

   P12 = P1-P2; P23 = P2-P3; P31 = P3-P1;
   t = sign(det([P31;P23]))*sign(det([P3-P;P23])) >= 0 & ...
       sign(det([P12;P31]))*sign(det([P1-P;P31])) >= 0 & ...
       sign(det([P23;P12]))*sign(det([P2-P;P12])) >= 0 ;

Point P lies within the triangle if and only if t is true.

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T A 2018-11-26

编辑：T A 2019-8-7

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UPDATED FOR CLARITY

With regard to assessing whether a point is on an edge/edges using the conditional statements given in Roger's answer,

P is on a triangle edge when one of the three conditional statements is zero
P is on a triangle vertex when two of the three conditional statements are zero

With regard to computational efficiency, the process can be costly if you're searching across many triangles. In such a case, the easiest thing to do is to only perform the calculations when P is within the bounding box of the current triangle:

Ptri=[P1;P2;P3];
if P(1)<=max(Ptri(:,1))&&P(1)>=min(Ptri(:,1))...
 &&P(2)<=max(Ptri(:,2))&&P(2)>=min(Ptri(:,2))
   %do the suggested calculations...
end

Evaluating this conditional statement is very, very cheap.