shadow help on simple school exercise

[prese]

Good morning to all and thank you for welcoming me in the forum.
I know I'm a little out of place, but I don't find a forum so rich in skills like this online.
school exercise that I carry under, is disputed that the shadow on the face of the pyramid marked with x. only to understand, no polemical intent, help me understand why the shadow would go.
from my point of view the "light beam" coming from the same angle of the base edge (30 degrees) but from the top (20 degrees), and being that side tilted upwards, this seems to me to be exposed to light, not in shadow.
What do you think? Where am I wrong?
Thank you! ;-)

 

[Tristus]

You're wrong when you create the shadow cone.
to verify it draws a line that goes top of the pyramid up to the center of the basic rectangle (the one identified by the intersection of the two diagonals of the rectangle). draw a horizontal line from that point (line that will indicate the direction of the beam of light). then traces a line that starts from the top of the pyramid, parallel to the inclination of the beam of light (i.e. 20 degrees) until you meet the horizontal line that starts from the center of the pyramid. merge the point so found with the bass of the rectangular base.
finally join the b c points, that will be the shadow cone. the triangle abc will be the cone of shadow

I gave it up with the photoshop but it's a slaughterhouse, but from that cone it is evident that the facade marked with the x remains in shadow.

 

[Tristus]

the shadow cone you designed would be correct if the direction of light was perpendicular (or almost) to the greater side of the basic rectangle.

 

[prese]

thanks tristus!!
You don't know how grateful I am.
the procedure that you suggest is that used for the first two solids, because in that case it was necessary to apply 30° "from the top" and 0° on the "support plan" in the first case, 40° "from the top" and 0° on the "support plan" in the second case, or always 0° on the base points.
in this case instead they are required 30° on the base (a corner that looks randomly coincides with the corner of the basic edge of the incriminated face. the prof in fact does not report an error on the shadow "on the ground", but the lack of the shadow on the side indicated with the x.
I hope I explained. ...
again, thank you! !

 

[Tristus]

with regard to the shadow on the facade, imagine making a tot horizontal sections along the entire height of the pyramid (as the foremen do when "segano" the model that is inside a trunk standing, inserting metal plates). if on the first section (that at the base of the pyramid) a shadow is projected... equally will happen for all other sections placed up. So you can say that all that facade will be in shadow.

 

[prese]

with regard to the shadow on the facade, imagine making a tot horizontal sections along the entire height of the pyramid (as the foremen do when "segano" the model that is inside a trunk standing, inserting metal plates). if on the first section (that at the base of the pyramid) a shadow is projected... equally will happen for all other sections placed up. So you can say that all that facade will be in shadow.

I think it is true that there is no shadow. the light comes from above (with inclination 20°) on the sloped plane of the face, I do not see the shadow... You do?

 

[Tristus]

then in the case of the rectangular pyramid the beam of light is almost perpendicular to the greater side of the base?

 

[prese]

then in the case of the rectangular pyramid the beam of light is almost perpendicular to the greater side of the base?

exactly, it is perfectly perpendicular.

 

[Tristus]

I think it is true that there is no shadow. the light comes from above (with inclination 20°) on the sloped plane of the face, I do not see the shadow... You do?

If the beam of light is perpendicular to the greater side of the base of the pyramid then the shadow cone you designed would be correct. I thought you had marked those 30 degrees to indicate the angle between the side and the direction of the beam of light.

with regard to the other inclination, that on the zenit, that determines only the length of the shadow cone projected on the ground.

 

[gil]

My personal curiosity. based on what norm and/or standard are these designs made?

 

[ceschi1959]

thanks tristus!!
You don't know how grateful I am.
the procedure that you suggest is that used for the first two solids, because in that case it was necessary to apply 30° "from the top" and 0° on the "support plan" in the first case, 40° "from the top" and 0° on the "support plan" in the second case, or always 0° on the base points.
in this case instead they are required 30° on the base (a corner that looks randomly coincides with the corner of the basic edge of the incriminated face. the prof in fact does not report an error on the shadow "on the ground", but the lack of the shadow on the side indicated with the x.
I hope I explained. ...
again, thank you! !

I have made a cad simulation and in fact I do not seem to be shadowed on the face, in the image that you place you can see that the red line that unites the base summit at the end of the shadow is inside the face that is then illuminated.
the same thing you can do with your design, if in fact you have not been challenged the projected shadow, just join the two points and you will see that the line goes into the face.

 

[Tristus]

probably it is only a theoretical question, meaning the faces affected by light beams that run parallelly along the same... not illuminate them, therefore they would be to be considered in shadow.

We would actually see those lighted faces anyway, but theoretically they are not. I assume it's just a theoretical dispute.

 

[Tristus]

from my point of view the "light beam" coming from the same angle of the base edge (30 degrees) but from the top (20 degrees), and being that side tilted upwards, this seems to me to be exposed to light, not in shadow.
What do you think?

take into account the fact that, when we come, for our convenience, to a schematization of light (think of the rays of light that hypothesized cuttings to calculate the height of the pyramids of giza) we consider such rays as lines that, starting from a light source, are parallel to each other regardless of the distance between the object and the light source. This by convention.
so the fact that the face is tilted does not affect.
It is true that the light comes from above, but the rays (by parallel convention between them) run parallel to the face, so they do not determine shadows even if the face is tilted.

Clearly, we're schematicizing. in the real world the light is made of light bounces, illuminated surfaces indirectly, etc., but when we want to apply geometry to light we have to schematize things in this way.
for greater realism we should also take into account the distance between light source and object if the light source is close to the object.
In this case, instead, a distant light source is hypothesized as the sun for which light rays are considered to affect an object as parallel to each other, so it indicates a single line as direction, as it is marked in the first drawing that you post

 

[prese]

I have made a cad simulation and in fact I do not seem to be shadowed on the face, in the image that you place you can see that the red line that unites the base summit at the end of the shadow is inside the face that is then illuminated.
the same thing you can do with your design, if in fact you have not been challenged the projected shadow, just join the two points and you will see that the line goes into the face.

Thank you baskets1959 I never thought I'd find people willing to treplicate on cad... Thank you very much!! !

 

[prese]

My personal curiosity. based on what norm and/or standard are these designs made?

school exercise.... I don't think we refer to any norm... .

 

[Tristus]

pyramid and shadow make come in mind cuttings, which compute the height of the pyramid by adding the shade measure to the middle of the base side of the pyramid (in your exercise half the lower base). of course he made a proportion between the length of the shadow drawn to the ground by a known height pole and the shadow drawn to the ground of the pyramid.
Talite knew that the pyramids are oriented in such a way that at some point the rays of light would have hit a face perpendicularly. at that point did his measurement, otherwise it would not have been possible to measure the height of the pyramid by that method.