Calculations of the length of the edges of a triangle, the normal vector, the area and the angles - Analytical Geometry with POV-Ray - Samples

Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmueller

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Systems of Coordinates
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- Samples from
Analytical Geometry
- Parallelogram of the
Middles of the Edges
- Trace Points of a Straight Line
> Calculations
about a Triangle
- Area of a Parallelogram
and Cross Product
- Shadow of a Pyramid
- Hit a plane || yz-plane
- Angle of triangle & yz-plane

Analytical Geometry with POV-Ray

- Samples -

Calculations about a Triangle
Calculations of the length of the edges, the normal vector, the area and the angles

Calculations about a Triangle with POV-Ray
A triangle is defined by three points:

#declare A  = < 3.0, 0.0,-4.0>;
#declare B  = < 4.0, 3.0, 2.0>;
#declare C  = <-1.0, 2.0,-3.0>;

The following values we can calculate
with POV-Ray very easily:
The vectors of the edges:

#declare AB = B-A;
#declare AC = C-A;
#declare BC = AC-AB;

The normal vector:

#declare N = vcross(AB, AC);

and then by |N|/2
The area of the triangle:

#declare Area = vlength(N)/2;

The angles of the triangle:
(in degrees)

#declare Angle_A= VAngleD(AC,AB);
#declare Angle_B= VAngleD(-AB,BC);
#declare Angle_C= VAngleD(BC,AC);

Calculations about a Triangle
(length of the edges, normal vector, area, angles)
This scene for POV-Ray: ".txt" file or ".pov" file

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© Friedrich A. Lohmüller, 2008
www.f-lohmueller.de