Casting a shadow onto the curved surface of an arch?

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Casting a shadow onto the curved surface of an arch?

Postby S1m0n » Fri Jun 16, 2017 3:00 pm

I was going through the beginning parts of Framed Perspective Vol. 2 and I can mostly understand what Marcos is doing in the shadow casting chapters. However, there is this diagram that I'm not really getting. Here is the description of the diagram.
"Now the light source is coming from a different direction than in the other drawings. When key points for the shadow's edge are on the curved area of the arch itself (point F, as we will eventually find out), first project the point onto the vertical behind it (point AA), then bring it up to the surface of the arch following the process visualized here. This is essentially the same process that is used for shadows on inclined planes: Find the key point on the flat surface and then project it to the objects' surface."
fp vol 2 fig 1.35.jpg
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Re: Casting a shadow onto the curved surface of an arch?

Postby S1m0n » Fri Jun 16, 2017 3:08 pm

I don't understand why he created a box to get the point which the line to find F passes through. When Marcos talks about the "vertical" wall is that vertical wall actually imaginary? It's an arch so it's always curved, and so the vertical wall is actually just defined as the plane perpendicular to the ground plane. I think that's what he means but correct me if I'm wrong. After that I'm not sure how Marcos is using the "perpendicular to vertical wall" and "direction of light" lines to form that little triangle on the ground. How is he determining the depth to connect those two lines? Why is he extending the line from AA to the right and then pulling it down to make this box? I would love it if someone could explain this to me.
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Re: Casting a shadow onto the curved surface of an arch?

Postby S1m0n » Fri Jun 16, 2017 11:27 pm

I have made progress in figuring out the diagram but I haven't really fully understood it. Marcos is shadowcasting one point, A. To do that he has to make a "stick" going from point a to the ground plane. He then creates a line from the base of light source through the base of the stick. It hits the wall at bb, then goes up to create a vertical line that is ignoring the curve of the wall. Draw a line from the top of the light source to A and where it crosses this line you mark a new point AA. AA exists inside the wall and not on the arch, so it has to be projected to the curve of the arch.
Draw a line through AA that is parallel to the direction of light on the ground. Feel out with your intuition where this hits the wall and this will be point you draw a line through to find F. For some reason to draw this guide line properly you have to take into account the orientation of the wall. Use a line perpendicular to the walls orientation and cross it through the guessed point. Draw a line down from when it hits the same depth as AA. Where that line hits the ground plane you can draw a curve from that point through the line and it will eventually hit F. The result is the correct positioning of the mapped point of the shadow casted by the arch onto a curved surface.
This is my guess as to what is happening in the diagram but I still don't really understand if the box is necessary. It looks like the left curve serves as a guiding line for the one drawn to find F.
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Re: Casting a shadow onto the curved surface of an arch?

Postby S1m0n » Sat Jun 17, 2017 11:48 am

I've done some more work on the diagram and at this point I can explain every step. I was wrong in saying that you use your intuition to find the distance from point AA to the curve of the wall. You can use your feeling but the way to find it is to project the height of AA to the vertical on the right. Then use the rvp and draw a line through that point until it hits the curve. Use the point where the rvp line hits the curve and draw a line using the lvp. This will define the distance you need to stop at when projecting AA to the curved surface.
proof of finding the distance of aa from the curve.JPG
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Re: Casting a shadow onto the curved surface of an arch?

Postby S1m0n » Sat Jun 17, 2017 12:39 pm

To find the direction of light you need you need to find the new shadow vanishing point on the vertical under the light source. One way to approach this is to create a rectangular volume with the same height as AA and you can see where the direction of light on the ground crosses the bottom of that volume. Make sure it crosses the bottom twice. You bring those points up to the top and then drawing a line through those points to the line under the light source gives you the shadow vanishing point. The picture attached is slightly innaccurate because I'm using a very rough perspective grid constructed from the brewer method. It's more to show you what I'm talking about.
Proof of finding direction of light on a different level.JPG
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Re: Casting a shadow onto the curved surface of an arch?

Postby S1m0n » Sat Jun 17, 2017 1:15 pm

The reason why you need to take into account the orientation of the wall is that you're trying to find the y planes (planes going left) that define the curve of the wall. The direction of the light is not parallel to the wall, so drawing a curve from where it hits the bottom and where it is projected to the wall will not get you a line that accurately describe the curve of the wall. This means that you need to use a line perpendicular to the wall, which can be found by drawing a line through AA to the right vanishing point. Project a line from AA to the right using the left vanishing point. Where these two lines cross draw a line down until it hits the ground plane. This new point exists in the proper perspective relative to AA. Draw the curve that describes the wall using AA and this point until it hits the direction of light from the light source to AA. To draw the shadow simply fill in starting at BB going up and then following the curve.
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