[vtkusers] TriangleArea() return the not correct value.

[Masato Asou]

From: David Cole <dlrdave at aol.com>
Date: Wed, 3 Sep 2014 08:43:31 -0400

>> Error of up to 0.0000000000000001 is acceptable in my program.

> You have to be really careful with your code if you want/need to keep
> all your error levels close to DBL_EPSILON.

Thank you for your advice.
It has not been able to correctly represent the intent of my previous
email.

The following is a quotation from first email.

From: Masato Asou <asou at soum.co.jp>
Date: Fri, 29 Aug 2014 11:41:15 +0900 (JST)

> $ ./a.out
> TriangleArea(A, B, C):  0.00000000526835606386

Above is not acceptable error.
Below is acceptable error.

> TriangleArea(B, C, A):  0.00000000000000009839

Heron's formula and cross product are acceptable.

> CrossProduct(A, B, C):  0.00000000000000011168
> CrossProduct(B, C, A):  0.00000000000000012055
> HeronsFormula(A, B, C): 0.00000000000000011252
> HeronsFormula(B, C, A): 0.00000000000000011252
> RectangularTriangle:    0.00000000000000017012

Error due to the order of the vertex is lage calculation result of
vtkTriangle::TriangleArea(). Error due to the order of the vertex is
small heron's formula and cross product.

From: David Gobbi <david.gobbi at gmail.com>
Date: Thu, 28 Aug 2014 21:19:08 -0600

> Note that there is a difference in efficiency, because Heron's formula
> requires applying sqrt() four times, while VTK's formula requires applying
> sqrt() only once.

Why vtkTriangle::TriangleArea() doesn't use cross product?
Also cross product requires applying sqrt() only once.
--
ASOU Masato