Directed Activity: 1-Point Perspective of a Tiled Floor

Shape

Drawing 3-Dimensional Objects--Directed Activity: 1-Point Perspective of a Tiled Floor

Focus	Explore a 1-point perspective model of a tile floor.
Technologies	The Geometers Sketchpad and model 6_1Point.gsp.
Background	Figure 6.14 shows a 1-point perspective view of a tiled floor. In this view, the “parallel” sides of the tiles extending away from the viewer converge to a vanishing point. The other sides of the tiles retain the appearance of being parallel. Figure 6.14: Perspective View of a Tiled Floor
Tasks	1. List three contexts in real life corresponding to the view in Figure 6.14. 2. Why do the tiles appear to shorten from front to back in the distance? From left to right? 3. In model 6_1Point.gsp, move the Vanishing Point to different locations on the Horizon Line. What effect does this have on the view of the tile floor? How would you explain the different views in terms of your apparent location as an observer? 4. In model 6_1Point.gsp, move the Distance Line left and right. What effect does this have on the view of the tile floor? How would you explain the different views in terms of your apparent location as an observer? 5. In model 6_1Point.gsp, move the Horizon Line up and down. What effect does this have on the view of the tile floor? How would you explain the different views in terms of your apparent location as an observer? 6. Select Show All Hidden in the Display Menu. In the first black tile on the left, measure the distance from vertex to vertex along the left side. Do the same for the white tile immediately behind it. Compute the ratio of those distances. 7. Move the Vanishing Point to the left or. What happens to the ratio? 8. Move the Distance Line to the left or right. What happens to the ratio? 9. Move the Horizon Line up or down. What happens to the ratio? 10. Repeat steps #5, 6, and 7 using a different pair of tiles. Describe your findings. 11. What are the limitations of this model? Under what conditions does it fail?