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

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 all the Model Types

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)
Comparison of Hip Side Cut Angle Model Types

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
Wireframe Sketch illustrating the plumb planes passing through the Eave Lines and perpendiculars to the Eave Lines

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 10/12 Side of Roof

Tetrahedral and Post Type Hip Side Cut Angle Models
View from 7/12 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 Plan Angles: View of the level plane of the Plan Angles

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
Hip Model upside down ... Valley Side Cut Angles: View of the unbacked shoulder of the Valley Rafter


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
Lines and Angles seen in Plan View

Wireframe Sketch of Plumb Section Planes
superimposed on the Tetrahedra extracted from the Hip Roof
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
Bird's Eye View of the Juxtaposed Tetrahedra ... lines and Side Cut Angles formed by the Plumb Section Planes


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

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 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 8.5/12 Side of Roof

Post Type Model of Irregular Hip Rafter Side Cut Angles
View from 10/12 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 Plan Angles: View of the level plane of the Plan Angles

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
Irregular Hip Model upside down ... Irregular Valley Side Cut Angles: View of the unbacked shoulder of the Valley Rafter

Joe Bartok