Irregular Cross Vault formed by
intercepting Hyperbolic Arches

Arch heights (rises) and semi-axis b remain constant.

Values of y and values of parameter t at corresponding
Framing Points are equal.

Values of semi-axis a and distances to Framing Points
along the x-axis shear according to the formula:
Valley Run = Common Run ÷ sin Plan Angle

Slopes of asymptotes and slopes at corresponding
Framing Points are governed by the formula:
Valley Pitch = Common Pitch × sin Plan Angle

Graph of Rectangular Hyperbola
3D Sketch of Irregular Cross Vault formed by intercepting Hyperbolic Arches
Slope of Hyperbola at any Point
Wireframe Sketch and Plan View of Irregular Cross Vault formed by intercepting Hyperbolic Arches
Main Vault Hyperbolic Arch
Valley Hyperbolic Arch
Adjoining Vault Hyperbolic Arch
Joe Bartok