Record TTriangle3

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Multiline triangle description.

Check does the triangle define a correct plane in 3D space. That is, check does the triangle not degenerate to a point or line segment (which can happen when some points are at the same position, or are colinear).

Like a normal vector of a triangle (see Normal), but not necessarily normalized.

Normal vector of a triangle. Returns vector pointing our from CCW triangle side (for right-handed coordinate system), and orthogonal to triangle plane. For degenerated triangles (when IsValid would return False), we return zero vector.

Plane of the triangle. Note that this has many possible solutions (plane representation as equation Ax + By + Cz + D = 0 is not unambiguous), this just returns some solution deterministically.

It's guaranteed that the direction of this plane (i.e. first 3 items of returned vector) will be in the same direction as calcualted by Direction, which means that it points outward from CCW side of the triangle (assuming right-handed coord system).

For NormalizedPlane, this direction is also normalized (makes a vector with length 1). This way NormalizedPlane calculates also Normal.

For three points that do not define a plane, a plane with first three components = 0 is returned. In fact, the 4th component will be zero too in this case (for now), but don't depend on it.

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Transform triangle by 4x4 matrix. This simply transforms each triangle point.

Exceptions raised

ETransformedResultInvalid

Raised when matrix will transform some point to a direction (vector with 4th component equal zero). In this case we just cannot interpret the result as a 3D point.

Surface area of 3D triangle. This works for degenerated (equal to line segment or even single point) triangles too: returns 0 for them.

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Random triangle point, chosen with a constant density for triangle area.

For a given Point lying on a given Triangle, calculate it's barycentric coordinates.

The resulting Barycentric coordinates can be used for linearly interpolating values along the triangle, as they satisfy the equation:

Result.X * Triangle.Data[0] +
Result.Y * Triangle.Data[1] +
Result.Z * Triangle.Data[2] = Point

See also [http://en.wikipedia.org/wiki/Barycentric_coordinate_system_%28mathematics%29]

Access the points of the triangle. This is the same as accessing Data field, it is also the default record property so you can just write MyTriangle[0] instead of MyTriangle.Items[0] or MyTriangle.Data[0].