Images of Post Type 3D Model
of the Hip Rafter Side Cut Angles

Main Slope = 10/12     Adjoining Slope = 7/12
Corner Angle measured between Eaves in Plan View = 90°

Development of Post Type Model of the Hip Rafter Side Cut Angles
(Trigonometric Scale)


Comparison of all the Model Types ... Bird's Eye View
Models to left and center ... Side Cut Angles on upper shoulder of unbacked Hip Rafter
The Tetrahedra extracted from the Hip Roof (right) describe a backed Hip Rafter


Comparison of Hip Side Cut Angle Model Types ... Bird's Eye View
Plumb planes passing through the lines on the surface of the
Tetrahedral Model (left) will produce the Post Type Model (right)


Wireframe Sketch illustrating the plumb planes passing
through the Eave Lines and perpendiculars to the Eave Lines
superimposed on the Tetrahedra extracted from the Hip Roof


Tetrahedral and Post Type Hip Side Cut Angle Models
View from 10/12 Side of Roof


Tetrahedral and Post Type Hip Side Cut Angle Models
View from 7/12 Side of Roof



Employing the Post Type 3D Model
of the Hip Rafter Side Cut Angles
to describe the Valley Rafter Side Cut Angles

Hip Model upside down ... Valley Plan Angles
View of the level plane of the Plan Angles
The "eaves" now represent the intersecting ridge lines at the Valley roof peak


Hip Model upside down ... Valley Side Cut Angles
View of the unbacked shoulder of the Valley Rafter
The "eaves" describe the intersecting ridge lines at the Valley roof peak and the
"Hip Length" represents the Valley sloping down from the level plane of the Plan Angles



A Review of the Juxtaposed Tetrahedral Models
... their Relationship to the Post Type Model
Application to describe both the Hip and/or Valley Side Cut Angles

Lines and Angles seen in Plan View


Wireframe Sketch of Plumb Section Planes
superimposed on the Tetrahedra extracted from the Hip Roof


Bird's Eye View of the Juxtaposed Tetrahedra
illustrating the lines and Side Cut Angles formed by the Plumb Section Planes
intersecting the plane of the upper shoulder of an unbacked Hip or Valley Rafter



Unequal Roof Slopes, Non-Rectangular Corner Angle
Images of Post Type 3D Model of the Irregular Hip Rafter Side Cut Angles

Main Slope = 8.5/12     Adjoining Slope = 10/12
Corner Angle measured between Eaves in Plan View = 120°

Development of Post Type Model of Irregular Hip Rafter Side Cut Angles
(Trigonometric Scale)


Post Type Model of Irregular Hip Rafter Side Cut Angles
View of the upper shoulder of the Hip Rafter


Post Type Model of Irregular Hip Rafter Side Cut Angles
View from 8.5/12 Side of Roof


Post Type Model of Irregular Hip Rafter Side Cut Angles
View from 10/12 Side of Roof



Employing the Post Type 3D Model
of the Irregular Hip Rafter Side Cut Angles
to describe the Irregular Valley Rafter Side Cut Angles

Irregular Hip Model upside down ... Irregular Valley Plan Angles
View of the level plane of the Plan Angles
The "eaves" now represent the intersecting ridge lines at the Valley roof peak


Irregular Hip Model upside down ... Irregular Valley Side Cut Angles
View of the unbacked shoulder of the Valley Rafter
The "eaves" describe the intersecting ridge lines at the Valley roof peak and the
"Hip Length" represents the Valley sloping down from the level plane of the Plan Angles