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Understanding Spatial Sense: Drawing 3D Shapes and Views

This guide explores spatial sense through drawing methods of three-dimensional objects. You'll learn about oblique, opaque, and axonometric views, as well as single and double vanishing point perspectives. By understanding the transition from 2D lines and surfaces to 3D solids with length, width, and height, you will grasp how to visualize objects like cubes in different views. Practical exercises will strengthen your skills in interpreting and drawing 3D representations, enhancing both your comprehension and artistic abilities in spatial reasoning.

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Understanding Spatial Sense: Drawing 3D Shapes and Views

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Presentation Transcript

  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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