Perspective tutorial!

Hi there! 😀

There are really not many great ressources for linear perspective out there in the web, what I read on tutorials so far was either extremely dumbed down to the point of misinformation (Just make a horizon-line here, put 1 or 2 vanishing points somewhere on it, derpyderp :P) or it was a bunch of tricks accumulated to make production easier and faster, but didn’t really help with understanding perspective (I love doing 3D for overpainting and making perspective grids, but one’s gotta know the basics I believe)

Soooo, I am not an industrial designer nor an architect, just a guy that draws so take it all with a grain of salt and consult your local doctor to get your perspective checked by a professional.

Anyways, for ressources, I recommend 3:

The excellent _free_ online manual on , this text is where I go to to fill in knowledge gaps, it is not very userfriendly, though. The language is quite convoluted.

For Architects there is the book from Gill: , it deals with drawing from plans and elevations and has neat step-by-steps to follow through.

and there is the Scott Robertson perspective book I see a lot of designers and concept artists recommending: , I haven’t read that one, but I hear it’s very good for designers and such. Also, James Gurney recommends it, so it’s probably an alright book.

Let’s start then! What I am going to demonstrate is drawing a cube with the “visual ray” method, which means I’ll not be using plans but measurepoints to handle the space. The way I see linear perspective is basically through the rotation of the object I am drawing relative to the observer. That means I am not thinking in horizon lines and 1-3 point vanishing points, although these are a logical consequence.

Whatever, let’s draw that cube, shall we?

1- point perspective


first, we need a good setup for our perspective drawing. For that I define a point and a circle around it (here in yellow). The mid-point is the center line of vision, which is where we are looking at directly. the circle around it is where we are standing. Every point on the circle can be seen as the view point, which may be kind of weird. for now we only use the point directly under the CL as our viewpoint though.

The circle in cyan would be our cone of vision. From the viewpoint the radius is described by an angle of 60°. That is to make sure we know where the perspective-distortions are going to be of major concern. We should try to keep our cube within this circle for it to look the most familiar.



Now, since we want to draw our first cube facing us straight, without any rotation we define the CenterLine as our sole Vanishing point. Every vanishing point has 2 measure points, which we need to draw diagonals. The first two Measure points are drawn by using the left and right points on our big circle (We will call it the 90° circle from now on). The lines coming from the measure points to their single viewpoint angle always at 90°.



Next, we draw the first edge of our cube. Since it is facing us, we draw a horizontal line with the length that we want to have. the red lines indicate were the other edges springing off this will go to.



In the following step we draw the vertical edge of the cube which has the same length as the horizontal one. In the future I will not post extra pictures for a step like this.



Now, to know where to put the edge in space we draw a line across from the horizontal edge to the measure point, since this is a diagonal, it will show us where the edge facing away from us will end.


Then we can just connect lines around and voilá, first cube drawn 😀


2-point perspective


Well, next thing we want to do is rotating the cube the way the picture shows, I guess the axis would be the vertical axis. The picture is a bit inaccurate, since the axis we will use is not the local axis of the cube, but the global axis of the viewport.


Anyways, what we are going to do is rotating the 90° angle we had going from the Viewpoint before to the measure points, and rotate that around a bit till it hits 2 new points on that central line, which we call a vanishing line, or, in this case, the horizon line. Those two points will be our 2 new vanishing points for the rotated cube.



So, since one edge of the cube is still facing us, we draw lines to the vanishing points from the foot of that edge.



Next thing we need is the measure point of those vanishing points. We start by taking the right Vanishing point and take the same distance, it has to the viewpoint on the horizon line (I did that by drawing a circle with the vanishing point as center and the distance to the viewpoint as radius. We then use the horizontal edge of the previously drawn cube as our measure bar, meaning taking its fixed length and connect it with the measure point to find out where the first edge of our new cube will be (Drawn in green)



We do that then with the measure point  of the other vanishing point, and then fill in the rest of the new cube. (the measure bar had to be moved to the left this time)


After removing all the construction lines, we have our second cube! Slightly rotated, so we see it in 2-point perspective.



Nadir/zenith perspective


Before we tackle 3-point perspective, I will go and use our first cube, from the beginning and rotate is on the other axis. This time, the horizontal. What that does, is create a 2-point-perspective situtation with vanishing points below (nadir) and above (zenith) the CL.



We want to rotate this cube so that one edge is going to the vanishing point above, VP3.


Consequentally, the other vanishing point is being constructed through the right angle from the viewpoint. (this time, our viewpoint is to the right, remember what we said earlier about the 90° circle)



We are now, like before, constructing the measure points for these vanishing points. The constuction lines are marked in red.


After doing that, we connect the lines for the cube.



3-point perspective

Well when we combine these previous methods by rotating the cube on two axes simultaneously, we get to have a 3-point perspective setup. Which means, we have to adjust our setup accordingly.



First of all, by choosing our vertical vanishing point up there, we also choose the horizontal line, where the other 2 vanishing points are going to be positioned. We do that by using the viewpoint again as center to draw a right angle to the vertical line.



On this new vanishing line (indicated in green), we need to establish our other two vanishing points. For that, we need a new point to determine the 90° axis. Something like an auxiliary viewpoint.

This we find by drawing a circle with the new central point as center, and the leftmost point of the 90° circle as the radius. Were that new circle (green) hits the yellow vertical line, there is the new anchor for the 90° which we use to determine our other 2 vanishing points.


connecting these three points leads to the vanishing triangle, which is a characteristic setup for 3-point perspective.

All 3 of the sides of the triangle is a vanishing line of the two corresponding vanishing points.



Just to make sure that the points are drawn right, we check by making lines through the center into the vanishing points. Each of the lines should hit the opposite vanishing line in a right angle. This is a helpful property of the vanishing triangle and serves to check if the setup is sound.



In the next step, we find the viewpoints of each of the vanishing lines. We already have the AVP(Auxilliary viewpoint) of the bottom vanishing line, the other two AVPs can be found through the respective vanishing points (remember, the AVP and the 2 Vps form a right triangle).



Next, we draw our measure bar 3 times at one point of the new cube. Each iteration is parallel to one of the vanishing lines.



now, we draw construction lines to the measurement points. We find those, if we draw a circle through a vanishing point to its auxilliary viewpoint. The result is the new measurement point for that vanishing point.


(In red, drawing lines from the edges of the measure bars to the corresponding measurepoints.)


After doing that, we use previously gathered skills to make this new cube a reality (blue)


aaaaand here we go, after all this, we managed to draw a perfectly well constructed cube in 3-point perspective!


For everyone wondering, there are 3 axes to rotate and object on, rotating the 3rd axis is something we did not do yet


It’s very simple though. Since the axes we were rotating on are global, which means inherent to the setup, this axis means merely rotating the setup itself. After the other 2 things, its pretty easy, really. Since we are dealing with a 2-dimensional surface and this rotation is the sole one really done in that space without any further projection.


So, sounds complicated and probably is. Whatever, understanding perspective also means understanding the shortcuts. But that’s just my opinion. Oh, and just if anybody asks, yes, this is math. The oldest kind, in fact. Euklidian geometry.


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