## Tuesday, May 15, 2012

### Steps To Extract a Tetrahedron In Google SketchUp

Creating roofs in Google SketchUp in 3D is fairly easy, but sometimes you need more roof framing angle information from your drawings. Here is a step by step example of extracting a  tetrahedron from a 3D drawing in Google SketchUp . In this example we'll use the Trapezoidal Timber generated from the Roof Framing Geometry plugin based on the Skewed Rafter on page 52 in "Traité Théorique et Pratique de Charpente" by Louis Mazerolle. This tetrahedron extraction is also an example of   "trait carré"  , drawing a perpendicular line to a given line.

Step 1.
Use the protractor tool and draw a perpendicular construction line,"trait carré", on the top edge of the rafter from point E.

Step 2. Draw a line from point E to point C and then delete the construction line made by the protractor tool.

Step 3. Use the protractor tool and draw a perpendicular construction line ,"trait carré",on the side of the rafter at point C. Then draw a line from point C to point A and then delete the construction line made by the protractor tool.

Step 4. Select the 3 top edges of the tetrahedron. Line E-C, line C-B and line C-A. Use Edit/Copy then Edit/Plaste.

Step 5. Draw a line from E-A and draw a line from A-B to complete the edges of the tetrahedron.

Step 6. Use the paint bucket tool paint the faces of  the tetrahedron. Then check the angles on the extracted tetrahedron to make sure they match the angles on the rafter.

Step 7. To draw the tetrahedron unfolded start by drawing a construction line at point B using the angle EBC.

Step 8. Draw a construction line at point E using the angle BEC. Then draw over the construction lines with the Line tool and then delete the construction lines made by the protractor tool.

Step 9. Draw a construction line at point C using the angle ECA. Draw a construction line at point E using the angle CEA.Then draw over the construction lines with the Line tool and then delete the construction lines made by the protractor tool.

Sometimes you need to use the protractor tool at a different location to draw the correct angle. After you have drawn the correct angle with the protractor tool use the move tool to place the construction line in the correct position.

Step 10. Draw a construction line at point E using the angle CEB. It helps to paint the face of the triangles to get the protractor tool to position it self correctly on the face of the triangle. Draw a construction line at point A using the angle EAB.Then draw over the construction lines with the Line tool and then delete the construction lines made by the protractor tool. Then paint the face of the triangle.

Step 11. Draw a construction line perpendicular to the line EA. Then use the Move tool and position the construction line at point C.
Step 12. Draw a construction line perpendicular to the line AC.  Draw the angle BAC at point A.

Step 13. Use the Tape Measure Tool and get the length of line CB. Then use the Tape Measure Tool again along the construction line at point C, to mark off the length CB. In a 2D Cad program we would use the Arc or Circle tool to mark off the location of the new point, but not in Google SketchUp. Then draw a line from D to the new point B.  The triangle DCB is the triangle that we'll use in the next post on Tetrahedrons.