Timber framers are familiar with geometric methods of determining angles in a complex roof. Trigonometry has a place in programming worksheets and calculators for quick solutions to any desired degree of accuracy.

    Although somewhat more abstract than the above two mathematical tools, the vectors and matrices of linear algebra will also solve angles. Applied properly, these techniques will solve problems which deviate from the Pitch / Pitch / Deck Angle norm, and are often otherwise intractable.

    More information on linear algebraic solutions to joinery problems may be found by linking to COMPOUND JOINERY , and opening Alternate Convergent Joint Solution or Compound Joinery Essay.

    ANGLE CALCULATORS  links to the Excel worksheet Working Point Co-ordinates, which will calculate the initial and terminal points of vectors in a Standard kernel. The script for the Framing and Joinery Angle Calculator employs vector products to solve joinery angle values.

    Click on the following links to open the Vector Products Calculator , or to learn how to use the determinants of matrices to solve cross products.

Vector Endpoints.pdf

Vector Components.pdf
Vector Components.doc

Direction Cosines of perpendiculars to Roof Planes.pdf
Direction Cosines of perpendiculars to Roof Planes.doc

Purlin related Hip-Valley Roof Solutions.html

Miscellaneous Hip-Valley Roof Angles.html

Square Cut Fascia intersects Hip Rafter.html

Layover Roof intersection - Irregular Plan Angle.jpg

Non-Rectangular Sections.pdf
Non-Rectangular Sections.doc