At 1:14 at 'A square in 2-point perspective': There are 3 lines arbitrarily drawn, and then the fourth one you get with the inbetween lying vanishing point it seems. But how do you get him? Is there an easy geometric way? I can only guess him it seems

@cskeers

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Lines 1 and 2 are drawn arbitrarily. They determine the front corner of the box. Line 1 extends all the way out from the vanishing point and doesn't do anything to determine the width of depth of the box. Line 2 is drawn out to the other vanishing point and stops whenever you decide you want the box to be just that wide. Now you can extend a line back from the corner created by 1 and 2 to the diagonal vanishing point (DVP), which in this construction is probably halfway between the first two vanishing points. This is the 45 degree diagonal across the square. He doesn't number this line, I guess because it doesn't make up any part of the boundary of the square. Line 3 extends from the end of line 2 back towards the first vanishing point until it crosses the line to DVP. At this point of intersection is the back corner of the box. Now just connect a perspective line from the off-page vanishing point through this back corner and where it intersects line 1 will be the final corner and complete the square. Check out Jay Doblin's book on perspective for some very helpful constructions for cubes. It's short, to the point, and free online. Just skip the math parts of they're confusing.

@philippfrogel9355

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@@cskeers thank you very much! But the DVP is just 'guessed', right? Or can he also be constructed somehow?

@cskeers

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It's halfway between the other two vanishing points on the horizon.

@philippfrogel9355

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@@cskeers but this halfway, it usually is not exactly halfway in terms of half the distance. I do not know a way other than guessing to find him. Do you know another way?

@cskeers

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@@philippfrogel9355 Actually for this construction (which is called 45 degree perspective) the DVP is conveniently halfway between the two vanishing points measured directly on the page. For vanishing points that are 30cm apart, it is at the 15cm mark. That's why this is the construction that people usually use. It's dead simple to construct, even without tools. Just eyeball the halfway point and it will be good enough. The problem, which he shows in the lower right corner, is that as the squares get further away from the DVP either to the left, right, up or down, they will start to get pretty distorted. The other thing that he doesn't cover is how to get the vertical dimension to create a true cube. Since both sides of the 45 degree cube are foreshortened, you either need to make a good estimate of the height of the cube, or use a construction to establish the true height. Other methods that will produce cubes in different orientations don't necessarily start with the vanishing points or the DVP. It's more like you would follow some other steps for building the cube in perspective, and then based on the cube that you create you could determine the DVP if needed. The only reason the DVP is used in this construction is because it is so easy to find in the special case of 45 degree perspective. As I mentioned above, check out Jay Doblin's book Perspective: A New System for Designers if you want to see the steps for getting the proper height, or producing cubes in different orientations with less distortion. You'll need a compass and a protractor. Even just producing a few cubes with the tools for mechanical perspective will help you to understand what you're doing when you draw freehand.