Wednesday, May 7, 2014

Perspective - One Point Perspective - Using a Diagonal Vanishing Point

Constructing a perspective of a free-form object, or a bunch of misaligned objects is trouble, and should be done in a computer with a CAD and rendering program. If however you have a design that is regular and rectilinear, there are simple rules that will get you there without a lot of work.

A tiled floor of equal sized squares creates a repeating pattern across the width and depth of a room.

But, it also creates a regular diagonal pattern which establishes vanishing points to the left and right of the centered one point vanishing point. If the grid consists of squares, then you have set up a diagonal system that can be used to establish any floor plan shape. 

A grid of regular lines on an elevation can be used in the same way.

In the photo above the grid is not made up of squares, so a number of diagonal vanishing points are possible. If you know the relative distances of vertical and horizontal spacing you can set up a measurable grid. In any case such a diagonal set of perspective lines will give you a grid to hang your design on.
Oh, alright. A short bit of graphic instruction would help here…

Draw a square, and then draw a horizon line 2 or 3 “squares” above. Draw lines from each corner of the square to the horizon line immediately above it. Strike a diagonal (dotted white line) to a vanishing point a reasonable distance to the side of the horizon line (You can do this by eye; a post on distortion will follow). By drawing a horizontal line where the diagonal crosses the lines connecting the square to the horizon line above you establish the top of the cube (white with cross inside). Carry vertical lines (green)  down to the lower lines going to the horizon and you establish the bottom of the cube (red with cross inside). This last step can be done or checked by striking a line to the diagonal vanishing point from the lower right corner of the original square.

Fill in the cube with solid white and you have a cube facing you in one point perspective. Simple, dull, boring and surprisingly useful.

While a circle drawn in the front elevation is a true circle, a circle on the top (which is receding in perspective) is an ellipse. The cross helps to place the ellipse which I use a template when drawing in the ancient mode.

It is quite easy to multiply the cubes in any direction. The diagonal vanishing point defines all subsequent cubes.

As said before, the front face of the cube (or any multiple thereof) is a measurable surface easily marked with an elevation drawing.

More importantly, any front face is equally measurable and ready for an elevation marking.

The cubes can be extended left, right, up or down. The only limitation is distortion.

But here is the fun part of the endless cube. By striking diagonals to the vanishing point from the centers of each side you create a… cube seen in two point perspective! Yes, you will have to adjust the height to get it right, but practice will educate your eye.

Drawing elevations on the faces of this new cube is a little messy, but again, with practice and a good eye you can reproduce a two point perspective without doing a complete layout.

We’ve dealt exclusively with cubes up until now. What about cylinders? Well, we have already marked circles on the sides of a cube, so it is simple to consider the circles as the top and bottom of a cylinder.

Fill in the form, and voila! 

Shade and shadow are useful to make the cylinder believable, but that is for another time and another post.

Caveats, caveats, and excuses…

Knowing the relationship between one point and two point perspective is very useful when working on something simple, or sketching an idea. If you want to produce a serious perspective, or want to see what a form looks like from all angles, go immediately to your computer. My reason for writing these post on perspective layout is not to replace the computer, but to supplement your knowledge about what is happening in the computer. Too many architects and designers have never worked out a perspective layout, but have gone straight to the computer. In my experience a little hands on work is necessary to make the most of the computer programs available.

Yes, I’m an old fuddy-duddy.

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