1 point perspective, linear perspective, horizon lines, etc. can influence your perspective drawings. That somehow, 'this doesn't look right,' when it's done incorrectly. These are words that you may have heard or feel at some point in time regarding a perspective drawing. Let's fix that.
In order for a drawing that looks right, perspective must be accounted for more than any anything else. In a way, it is easy if you can visualize it. However, I never thought it is that easy. Neither should you. Despite that, it can be at least simplified.
To start, a simple 1 point perspective is a foundation for all effective drawing. The benefits are well known: you become a better artist and a more believable artist as you are able to show your understanding of complex perspectives to others through your drawings
More over, this perspective is used to build other complex perspectives whereby understanding difficult these concepts builds confidence. Don't you want to feel confident in your ability to draw and have that confidence shown in your art for others? I know you do.
So what is the first thing it can teach you? Figure A shows us a really important concept of measuring: the cube and the square. In it, you can fit whatever shape or object you desire whether it be a simple table or a well-proportioned human.
Figure B expands on that idea and goes into measuring a simple 1 point perspective using the cube. Notice the intersecting triangles? These become points for the size of the next square in the sequence. It will go on infinitely-shrinking every time it approaches the horizon.
Figure C is another look at the concept of distance from an offset point of view. You can see another vanishing point above the horizon creating a point of measurement. Note the size changes to the cube as the intersecting lines results in an accurate placement of key measuring lines.
Figure D is a practical look at this measurement. Regardless of what object you decide to fit into the cubes (a human, a table, etc.), you will get a rough idea where and when to distort you shapes as it approaches the horizon.
Figure A shows the construction of depth. In the center, you have your standard single point perspective creating the guide showing how objects shrink as it approaches the horizon. To further increase its accuracy, you will need to introduce two other vanishing points on either side.
Figure B illustrates what happens when all three points intersect: it creates a diamond that slowly compresses as it approaches the horizon. So, continuing with this concept, start to add more lines that intersect with the middle vanishing point.
Do you see what happens with Figure C? As you can probably tell, while the center diamonds are compressed, it creates 'rectangles' on the plane. What is neat, though, that these 'rectangles' are actual perfectly proportioned measuring squares in its own given spot on the plane.
Figure D shows another potential: the three point perspective. Just using the original single point perspective as a measuring point, you are able to construct other measuring points to create your perspective plane.
Moving vanishing points is a natural occurrence of perspective. Figure A shows this: an object at the very top has its vanishing point shown within the picture plan. However, its vanishing points shift outwards on the horizon as a means to not distort the box.
Figure B is an interesting take on deciding your picture plane. Whether it is tilted or not, you will notice that it does not go outside the boundaries of the 'lower triangle.' I find that this is a great compromise that allows for proper dynamic perspective without distorting your subjects.
On the same subject of horizon lines, Figure C shows an interesting situation of a false horizon. Think driving down into a valley. The true 1 point perspective will be the black line as points towards the farthest point in the picture.
But what if you can't see the horizon line? Figure D is an example of this. Think in terms of driving up a hill. In a car, what you see may look like a horizon line. However, the true horizon is on the other side of the hill. These things must be considered if your drawing is not a flat plain.
So now that you know how to measure and set your picture plane, what else do you need to know? I believe the last important concept regarding 1 point perspective is its importance in achieving depth.
Figure A shows three objects that are the same size and shape. Places in the center, you can see just how much of it is altered and what can be seen. That means you will need to understand how the top, front, and bottom of your subject will look like. What about more complicated shapes?
While it's ideal to place your object in a cube, Figure B shows a wine glass and how multiple different shapes are used to construct it. The depth created is vertical depth showing both the upper and lower sections of the glass. Again, this will change depending on its relationship to the horizon.
Figure C is an expanded concept of what we have talked about so far. The cubes may look different in size, but in fact, both cubes are the same size. It just that one cube is in front of the other one suspended in midair.
Figure D is the final example. Not only are you introducing a third perspective, but notice that the vanishing points appear on different anchor points. What does this achieve? Well, the left cube is not only longer, but it's also smaller.
In summary, this perspective is a great measuring device, an awesome grid making device, can exist in many different forms, as well as a remarkable tool for determining depth. With a little bit of practice, you can start to make the proper conclusions that work for you.