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You have a challenge ahead. You need to draw cubes without looking at cubes. Your friends should swear you copied them. Why do this? Drawing an accurate cube without reference gives you the most basic foundation for advanced perspective.

The Power of the Cube

Cubes provide three axes. These cover the world in all three dimensions. They use right angles strategically laid out to navigate every direction. The finale is the square faces. A square is the constant and true source of measure to eyeball proportions.

Up until now, we drew box forms without much concern for proportion. Now we want to perfect our foreshortening skills. We master proportion by seeing in simplified units. In perspective, we see in squares and cubes.

The Challenge of Proportion

It is easy to spot a square on a flat surface. Tip that flat surface in space and it becomes hard to discern. Foreshortened planes can surprise us. They lie in space. A tipped rectangle can easily look like a cube. Only the trained eye can control a true square in perspective.

Tricks to Check Your Proportions

Let's look at some tricks to build this serious skill.

• Extend lines: A small deviation gets big if it keeps extending. A two-degree error reveals itself the further you draw it. Extend a foreshortened square to see if it is truly square.
• Check the far plane: The hidden far side of a cube is less foreshortened. The less a plane foreshortens, the less it distorts. Look at it and adjust. Estimate first, then refine with that distant plane in sight.
• Draw through the box: This is a reliable way to check your proportions while sketching.
• Place circles: A square and a circle touch at four points. They stay fixed when you tip the drawing in space. Foreshortened circles become ellipses. These ellipses can give us the proportions of a foreshortened square.
• Find diagonal vanishing points: We want to imprint the 90-degree angle in perspective. Another good angle to know is 45 degrees. Only a square gives us perfect and easy-to-find 45-degree angle diagonals.

Training Your Mind's Eye

When drawing your cubes, rehearse the three-line systems. Remind yourself that each line goes in the same direction as its neighbors. Assess each square in perspective with a critical eye.

On every square, run lines from corner to corner. Run lines across horizontally and vertically to divide the faces into segments. Out loud, remind yourself where the 90-degree and 45-degree angles sit in perspective. This prepares you to see a protractor in space.

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