A student wrote me asking how he could make a SketchUp model that realistically represented a project he built in the shop. The project is a lampshade constructed of four L shaped risers and horizontal stretchers.
In the shop he started with four risers, each glued up to produce the L shape. He tied two sets of the risers together with a stretcher. The results are in the picture at left.
The student didn’t share his thoughts behind his question with me, so what follows is my interpretation of what he may have been thinking.
He may have wondered why the left and right sides of the L were not 90° to the sides. Being curious he may then have produced a SketchUp model, perhaps to answer his question. The SketchUp model produced desirable results as seen below right. Clearly all the side are right angles. He wondered why the difference and asked if I could produce a model that represented “reality” – i.e. the shop version.
The simple answer as to why these models are different is that he built the shop model and the SketchUp model differently. The shop model started with glue ups at right angles and roughly 1” on a side and 3/8” thick. He then made a compound cut to allow the risers to tilt inward in both the x and y direction.
The problem is that when you tilt the risers in both direction and then tie them together with a stretcher, which itself is tilted inward, you force the other side to point inward. Further, when you cut the L shape with a compound angle you produce a cross section that is not rectangular, but rather parallelogram in shape. You can see this nicely in the photo thanks to the glue lines. Click on the photo to enlarge it and look at the pieces joined together to form the L.
So why did the SketchUp model look so nice and provide the desirable results? The answer is found in a quote from the email he sent me.
SketchUp Model: To make the vertical risers – drew the bottom (L-shape) as a horizontal plane, drew a second "L" and moved it up and out, and then connected the corners.
He essentially made the assumption that a compound cut would produce a cross section with right angles, that is, rectangular in shape. He then produced the cross section he wanted and copied it at a higher elevation and shifted it inward in both x and y direction. Finally he connected the corresponding corners to form risers. A detailed inspection of the resulting riser would reveal that the angle between the outside faces would have to be greater than 90°; not by much. In fact little enough to deceive the eye.
I constructed a riser using this right angle assumption just as the student did. It was 1” wide on the outside faces, 20” high and tilted in 3” in x and y. The angle between the outside faces I measured to be approximately 91.3°.
I then constructed a SketchUp model using the shop model approach. That is, I started out with L shaped risers that was all right angles. Then I used slicing planes to cut the top and bottom just as you would do with a compound miter saw. Then I rotated the risers in the x and y direction to align the compound cuts with the ground plane (red/green plane) and achieved the desired tilt. The resulting picture is at left.
This model is tilted a lot to demonstrate what happens. The only reason this model does not look exactly like the shop picture above is because I did not tie riser sets together with stretchers and force the front and back faces to align. If I had the side faces would be angled in even more. You can download this model and convince yourself that the risers are in fact constructed from right angle stock and compound mitered at the ends.
Compound miters, or more generally, faces that are at angles to two planes, are a difficult problem for most people starting out with SketchUp to master. If you have taken my beginner’s and intermediate SketchUp courses you have heard me talk about slicing planes. This problem begs two questions: how do you create the correct compound slicing plane to achieve the desired splay and what angles do you set your table saw, or compound miter saw for when cutting them. I will answer the first question in the attached video below. The second question is the subject of a subsequent post. Stay tuned.
A Related Tutorial Video – Drawing Tapered & Splayed Legs
Drawing Tapered & Splayed Legs is a related tutorial video you may also be interested in.
Viewing The Video
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Full Screen Viewing
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