To divide a square or cube by any number:
- draw a line extending from one corner.
- measure equal distance for however many points you want to divide it by (in the below example, I’ve used 3).
- Take the final point to the opposite corner.
- For each remaining point, draw lines parallel to the first one to find their mark on the cube or square. In the case of the cube, you can take these marks back to the vanishing points and all the way around the cube.
- To find the vertical divisions, draw a diagonal line across the face. Where this line intersects the other lines is where the vertical divisions will be.
To draw an object in perspective using measuring points:
- Put vanishing points on the horizon, then divide it into eighths. For a 45 degree angle, the front edge of the shape will be on the halfway mark. For a 30/60 degree angle, the front edge will be on the 1/4 or 3/4 mark.
- Create a baseline. This will dictate the vertical angle of view.
- Under the baseline, draw two orthographic/elevation/2D views of the object.
- The vertical front edge is the only ‘true length’. Therefore the height of the 2D shape will be the same as the height of the front edge of the cube.
- From here, you can run lines back to the vanishing points to find the side faces.
- This is where the measuring points come in:
- For a 45 degree view, the right measuring point is at the 1/4 mark (on the left-hand side) and the left measuring point is at the 3/4 mark (on the right-hand side).
- For a 30/60 view on the left of the page, the right measuring point is at the 1/8 mark (on the left hand side) and the left measuring point is at the 1/2 mark. This is flipped if the front edge is on the right side of the page.
- Now the vertical lines on the 2D views can be taken up to the baseline. From the baseline, they will be taken up to the measuring points on opposite sides.
- Where these lines intersect with the face of the cube is where they can be taken up vertically to find the outside edges of the shape.
- Measuring points will only work for vertical lines. Horizontal lines will need to be worked out using the division methods outlined above.
The measuring point method can also be useful without orthographic projections. As you can see below, it can be used as another way to divide a cube or to create a grid out of multiple cubes.
Some weeks after learning this method, I was able to use it to draw something like this: