1. Two-Point Perspective
During the Renaissance artists became very interested in making two-dimensional artworks look three-dimensional. They used mathematics and close observation to invent “Linear perspective"—a technique that allows artists to trick the eye into seeing great distances or 3-D forms in a 2-D artwork.
Linear perspective allows artists to trick the eye into seeing depth on a flat surface.
Viewing Point: The place where you are, your eye level.
Viewing Angle: The place where you are, your eye level and the angle from your point of view.
Viewing Height: The place where you are, at your eye level and height or elevation.
Horizon Line: That place where the land and the sky meet.
Picture Plane: A make believe paper or canvas between you and the work you are illustrating.
Vanishing Point: The single point on the horizon where all the lines on the ground level seem to be coming together.
Single Point Perspective: A single vanishing point on the horizon line.
Double Point Perspective: Two separate vanishing points on the horizon line.
Triple Point Perspective: Two vanishing points on the horizon and one in the sky or on the ground.
Light Reference: The point where your light source comes from for example the sun or a lamp
Shadow Vanishing Point: A point directly under your light reference and on the horizon line or on the ground.
Foreshortening: To shorten the lines of (an object) in a drawing or other representation so as to produce an illusion of projection or extension in space.

2. Why can’t we just guess?
Many earlier artists were interested in showing depth, they could see the objects receded into space and so tried to copy the effect, but the results were not always accurate.

3. 2 point Perspective
Perspective is a realistic way of drawing objects in 3D. We have already looked at single point perspective in Foundations 1. Now lets look at Two point perspective (using two vanishing points).
When an object is drawn using two or more vanishing points, it is even more realistic than if it were to be drawn with a single vanishing point because we rarely view our world from a single angle.

4. Perspective is the ‘Science of Art’.
Two-point perspective is useful to show an angle rather than face-on.
In perspective, most lines are vertical or ‘orthogonal’ (right angles) drawn to two different vanishing points.

5. Now watch the illustration and see if you can learn the pattern for drawing a cube in two point perspective.

6. Now it’s your turn:
1. Turn your paper horizontal ("landscape" orientation)
2. Line the end of your ruler up with the side of your page.
Be sure the ruler is straight and flush with the edge of the page or everything will be crooked!

7. You may prefer using a triangle to draw horizontal and vertical lines
You may prefer using a triangle to draw horizontal and vertical lines. Just make sure it is correctly placed!
3. Draw a horizontal line one or two inches down from top of the page. This is your horizon line.

8. 4. Draw two dots on your horizon line near the edges of the paper
4. Draw two dots on your horizon line near the edges of the paper. These are your vanishing points.
5. Draw a vertical line that is the "front edge" of your form.

9. Draw lightly so you can erase!
6. Connect the two ends of your "front edge" line to each vanishing point. These are called orthogonal lines.
7. Draw two vertical lines between the orthogonal lines where you want the back edges of your form.
Remember: In two-point perspective most lines are either vertical or orthogonal. There are rarely horizontal lines in two-point perspective!

10. 8. Now join the back, top corners to the opposite vanishing point to complete the top of the form.

11. 9. Erase the extra orthogonal lines
9. Erase the extra orthogonal lines. Now you have a simple form drawn in two-point perspective!

12. 10. Now add details and experiment!

13. Two Point Perspective distortion
When using two point linear perspective, one must look carefully at the placement of the object. If the object is not perpendicular and parallel to you and you are looking at it's corner, then you probably want to work in two point. Sometimes when working in two point perspective one of the vanishing points is not on the page. You then must approximate where the point falls by looking at the angles of the object which you are drawing. The best way to approximate an angle and find a vanishing point in two point perspective is to first find your horizon line. This is a level line. By using this level and placing it next to the front corner of the object one can then see the angle and continue this angle out until it intersects with the horizon line. After you have found this intersection, then you have established your vanishing point for all the planes that are parallel and recede the same direction. Repeat this process for the other side of your object and all convergence lines will be established. Use the font edge of an object in two point perspective when you want to scale it. This is the only constant line in two point because there are no horizontals on the object to work from. Verticals are always at a 90 degree angle to the horizon line in one and two point perspective.
Find your horizon line first. Then find out how much distance in proportion to the object's height there is between the horizon line and the front vertical edge of the object. This will help eliminate distortions.

14. Remember that you are working within a cone of vision
Remember that you are working within a cone of vision. Adjust your drawing so that all of the information is within this cone, otherwise you will have some distorted areas.

15. From Simple shapes to everyday objects
In this example a simple kitchen table is drawn in two point perspective. This is much more difficult compared to the single point perspective. This time it is very important to project guidelines towards both vanishing points.

16. More complex objects Vanishing point Eye level line Vanishing point

17. Another complex object
All objects have receding edges. Whether they are rounded or oval, or flat or wedged shaped, they all recede into the distance. Perspective is the method an artist uses to obtain more realism and depth in their drawings.

18. Even comic book artists find an appropriate application of perspective.
Cone of vision

19. Cylinders in perspective are also figured by using the eye level line and vanishing points. Notice how a cylinder fits into a square space.
ellipse
A circle in perspective is called an ellipse.

20. Your Assignment: 2pt. Perspective Building
Create a building structure with more than 20 windows and multiple rooms, etc, added on to the basic structure. It can be modern or historical, fantasy or actual. I must also have a broken roof line of added and subtracted perspective.

21. If you need Ideas or have a certain look you want to create, look at references. They will help you get the feel you desire to achieve in your drawing.

22. Your final may look something like these.
When you are finished with the perspective aspect, add value to create a more lifelike scene.
Do them in black and white or in color. It is up to you, but take the time to make them clean and professional looking.