1. Math 314 Spatial Sense

2. Topics Views Drawing Methods - Oblique - Opaque - Axiometric - Single Vanishing - Double Vanishing Solids

3. Views We are going from two dimensional to three dimensional. Lines have 1 dimension – length Surfaces have two dimensions length and height or length and width. By combining surfaces we can construct shapes that define a space called solids. They have three dimensions – length width & height.

4. 2 dimensional BACK RIGHT FRONT LEFT

5. Adding Cubes Now we can place cubes on the grid. The numbers represent the number of cubes. For the front view put one cube on the left side (1 st row, 1 st column) Put 2 cubes on the left side (2 nd row, 1 st column).

6. Cube Viewing 312 212 111 BACK RIGHT FRONT LEFT

7. Key for Success The key to these exercises is to ask yourself what is the most amount of cubes you see in a specific column Be careful when looking at rows and columns; it can be confusing!

8. Drawing a Front View 312 212 111 BACK RIGHT FRONT LEFT As we look at the left-most column we see 3 cubes Middle-1 cube Right – 2 cubes

9. Front View

10. Draw a right view Again, ask yourself… ask yourself what is the most amount of cubes you see in a specific column

11. Recall Original Figure 312 212 111 BACK RIGHT FRONT LEFT

12. Right View 1 st column = 1 2 nd column = 2 3 rd column = 3

13. Homework #1 a-j (Stencil)

14. #1 a 231 321 111

15. Homework Solutions 1a FrontRight

16. Work in Class P17 a1); the answer is… Left A2); the answer is… Top A3; the answer is… Front A4; the answer is… Bottom

17. Work in Class P18 c1 Front 3,1,2 – draw on board C2 right 3,2 C 3 back 2,1,3 C4 (top) 2,elevated 1,elevated 1 (draw on board!)

18. Work in Class / Homework P19 e 1-6 P20 g 1-6

19. Going backwards If we are given a front and right view can we give a top grid view? In most cases, the view is not unique (more than one answer) The trick is to start with 1’s (not 3’s) and move up…

20. Front Right GIVE TOP GRID VIEW

21. Top View 311/2 1 111 BACK RIGHT FRONT LEFT

22. Work in Class / Homework Stencil #2 a-e Do one more on board… 2a 1 ST 5 people to come see me for points!

23. #2a Solutions 31 / 21 111 3 1

24. Drawing a Cube We want to add a little more reality into our drawings Oblique Face parallel to the paper’s edges Receding lines reduced size (usually half) Face is in the foreground Disappears to the right; RIGHT facing

25. Drawing a Cube

26. Definitions - Prism Between two parallel planes and a polyheatron A congruent (equal) polygon in each plane called bases Lateral shapes are rectangles

27. Definition - Pyramid Between two parallel planes and a polyhedron A polygon in one plane called a base An apex in the other plane Lateral shapes are triagles

28. Cylinder Between two parallel planes and a curved surface A congruent circle in each parallel plane called base Continual lateral shape of a rectangle

29. Cone Between two parallel planes and a curved surface A circle in one place An apex in the other A lateral shape of a circle with an angle cut out of it.