Aspect Ratio

ratio1 = V1/H1

ratio2 = V2/H2

Skew value is larger of ratio1 or ratio2.

Skew

First, HyperMesh constructs lines connecting the midpoints of each edge of the quad (dotted in the picture below).  Next, HyperMesh constructs a third line (green in the picture below) perpendicular to one of the initial lines, then finds the angle between this third line and the remaining initial line--with which is it most likely not perpendicular, unless the quad is a perfect rectangle.

α is the skew (angle) value.

Taper

First, the quad’s nodes are projected to plane defined by the orthonormal vectors U-V found as follows:

Z = X × Y

V = Z × X

U = X

For each corner node, determine a vector from itself to the center of the quadrilateral. These vectors are along the plane formed U-V.

Consider the vertical sides: Calculate vectors along these sides by subtracting the red – dashed vector from that directly above it. This forms the two blue vectors. Find the angle between these blue vectors. Now, do likewise for the horizontal sides. The taper is the largest of these angles.

Warpage

This check applies only to quads or rectangular faces of solids.

Warpage = 100 * h / max { Li },

where h is the minimum distance between the diagonals.