MehemmedSettarli's blog

Triangle Area 2D
By MehemmedSettarli, history, 3 months ago, In English

I have given 6 triangle indexes in 2D and I don't know how to calculate the area of this triangle example (1 1, 2 4, 3 2) are equal to 2.5. Can anyone help me, please? I am keen to write it in C++.

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3 months ago, # |
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A = (1/2) |x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)|

A => Area of Triangle

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3 months ago, # |
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First, we can calculate the length of AB, AC, and BC using:

$$$AB = \sqrt{(B_x - A_x)^2 + (B_y - A_y)^2}$$$,

$$$AC = \sqrt{(C_x - A_x)^2 + (C_y - A_y)^2}$$$,

$$$BC = \sqrt{(C_x - B_x)^2 + (C_y - B_y)^2}$$$

Let's call $$$p = \frac{AB + AC + AD}{2}$$$

Area of triangle will $$$S = \sqrt{p\times(p-AB)\times(p-AC)\times(p-BC)}$$$

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3 months ago, # |
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Thanks a lot also i want to ask that how I can find the point lies on a segment or not?

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    3 months ago, # ^ |
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    Let's say that you want to check whether the point $$$C$$$ lies on the segment $$$AB$$$. Point will lie on the segment if and only if area of triangle $$$ABC$$$ will be $$$0$$$ and $$$|A_x-C_x|+|C_x-B_x|=|A_x-B_x|$$$.

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      3 months ago, # ^ |
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      thank you very much

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      3 months ago, # ^ |
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      I don't think that checking x coordinates suffices: what if the segment $$$AB$$$ is vertical and $$$C$$$ is on the same line but outside $$$AB$$$ (in other words, $$$A_x = B_x = C_x$$$)? We have to check a similar equation for y coordinates as well.

      Alternatively, after checking that the triangle $$$ABC$$$ has area of $$$0$$$, we can check if $$$\min(A_x, B_x) \leq C_x \leq \max(A_x, B_x)$$$ and $$$\min(A_y, B_y) \leq C_y \leq \max(A_y, B_y)$$$.

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        3 months ago, # ^ |
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        Yeah, you are right. Thank you for pointing out this error!

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