Perspective 7: 2 Point Views, Measuring, & Ellipses

[New Masters Academy]

Artist and veteran instructor, Erik Olson demonstrates additional views and scenes set ups using with “in picture” methods, which allow the artist to stay within the picture frame to set up correct perspective. Scale referencing on uneven surfaces is also demonstrated along with a digital draw over and the behavior and drawing of various ellipses and simple elliptical objects in 2 point perspective.

Materials

• 45-45-90 Transparent Triangle Ruler
• 30-60-90 Transparent Triangle Ruler
• Alvin Pro-Matic Lead Holder – 2H Lead
• Alvin Rotary Lead Pointer
• T-Square Ruler
• Protractor
• Prismacolor Verithin Colored Pencil – Red/Blue
• Paintbrush
• Kneaded Eraser
• Hard Eraser
• Helix Technical Compass

[Aidan Andrews]

is the method used to find the right measuring point MPR meant to be an approximation? I understand it working out to be about the same given how far out the VP is, but geometrically I don’t think it checks out…

[Andrew Hunt]

I didn’t believe it worked either, so I had to check with a smaller triangle. The points MPR, SP and VP R do actually form an isoceles triangle, so MP R to VP R = SP to VP R even though it doesn’t look like it. The center of vision caused my brain to not realize the isoceles triangle being formed, but drawing it out and measuring reveals it actually is one.

[Aidan Andrews]

In your drawing, the verticals which would form the base for the diminishment guides are already parallel to the base of the isosceles. So the line drawn through all their midpoints really does represent a bisecting line whose perpendicular forms the base of the isosceles, and intersects with HL to give us the point MPR. BUT in the lecture, the verticals which form the base for the diminishment guides are 90 degrees to HL, and so don’t form the necessary bisecting line needed to find point MPR.

[Aidan Andrews]

Ok so I’ve been puzzling over this on-and-off since I posted 2 months ago and it turns out the measuring points are always going to be 45 degrees apart with respect to the Station Point. I don’t know if this is already well known information but I didn’t find anything about it anywhere I’ve looked.

So the easier technique to find the measuring point of an off-page vanishing point would be to,

 

first: find the measuring point of the visible Vanishing point. (in the case of this lecture, measuring point left)

second: draw a line connecting this MPL to the SP.

third: Use your 45 triangle to shoot back up from the SP at a 45 degree angle to the drawn line; where it intersects the HL, you’ve found your measuring point right, MPR.

 

A while back I made this graph to try and understand the whole thing better. It’s here, https://www.desmos.com/calculator/kmd9ureoud

 

[Aidan Andrews]

here’s the proof I just finished:

[Aidan Andrews]

[Aidan Andrews]

[Aidan Andrews]

[Aidan Andrews]

and then redrew the diagram for clarity,

 

[Aidan Andrews]

My proof:

 

For the mathematically inclined. I’m sure there was a much simpler way but I didn’t find it.

Can’t wait for Erik in a later lecture to casually mention, “oh yeah and by the way there’s actually a 45 degree relationship–”

It was fun anyhow. Very useful.

[Aidan Andrews]

Also just realized as a consequence of the 45 degree relationship, the line connecting a measuring point to the SP is always going to bisect the angle formed by the line which connects the Vanishing point to the SP and the centerline.

so in terms of my above diagram, line DB will always bisect angle ABE and line FB will always bisect angle CBE.

So you can find both measuring points if you just do an angle bisection with your compass. No need to get a long piece of paper.

 

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