Cubeit 16.3 User Documentation
The metrics used for triangular elements in Cubeit are summarized in the following table:
Function Name

Dimension

Full Range

Acceptable Range

Reference

Element Area

L^2

0 to inf

None

1

Maximum Angle 
degrees

60 to 180

60 to 90

1

Minimum Angle 
degrees

0 to 60

30 to 60

1

Condition No 
L^0

1 to inf

1 to 1.3

2

Scaled Jacobian 
L^0

1 to 1

0.2 to 1

2

Relative Size 
L^0

0 to 1

0.25 to 1

3

Shape 
L^0

0 to 1

0.25 to 1

3

Shape and Size 
L^0

0 to 1

0.25 to 1

3

Distortion 
L^2

1 to 1

0.6 to 1

4

Element Area: (1/2) * Jacobian at corner node
Maximum Angle: Maximum included angle in triangle
Minimum Angle: Minimum included angle in triangle
Condition No. Condition number of the Jacobian matrix
Scaled Jacobian: Minimum Jacobian divided by the lengths of 2 edge vectors
Relative Size: Min( J, 1/J ), where J is determinant of weighted Jacobian matrix
Shape: 2/Condition number of weighted Jacobian matrix
Shape & Size: Product of Shape and Relative Size
Distortion: {min(J)/actual area}*parent area, parent area = 1/2 for triangular element
Relative Size, Shape, and Shape & Size are algebraic metrics, which
have well behaved properties. Cubeit encourages the use of these metrics
over other metrics. These metrics are referenced to an ideal element which,
in the case of triangular elements, is an equilateral triangle. Thus deviations
from an equilateral triangle are measured in various ways by the algebraic
metrics.
Relative size measures the size of the element vs. the size of reference
element. If the element is twice or onehalf the size of the reference
element, the relative size is onehalf. By default, the size of the reference
element is the average size of all the elements that the quality command
is currently evaluating.
The shape and size metric measures how both the shape and relative size of the element deviate from that of the reference element.