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Math 314

Math 314. Spatial Sense. Topics. Views Drawing Methods - Oblique - Opaque - Axiometric - Single Vanishing - Double Vanishing Solids. Views. We are going from two dimensional to three dimensional. Lines have 1 dimension – length

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Math 314

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  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 LEFT RIGHT FRONT

  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 (1st row, 1st column) • Put 2 cubes on the left side (2nd row, 1st column).

  6. Cube Viewing BACK LEFT RIGHT FRONT

  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 BACK • As we look at the left-most column we see 3 cubes • Middle-1 cube • Right – 2 cubes LEFT RIGHT FRONT

  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 BACK LEFT RIGHT FRONT

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

  13. Homework  • #1 a-j (Stencil)

  14. #1 a

  15. Homework Solutions 1a Front Right

  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 BACK RIGHT LEFT FRONT

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

  23. #2a Solutions

  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.

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