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Hey guys, currently I am wondering how to calculate the degree of the side plain towards the light source (marked with the question mark). Is it correct to guess this angle by looking at the cube from the top and make a guess at the correct angle ? if so then it seems a +- 45 Degrees. If 90 degrees is full lit (0) and 0 degrees is full dark than 45 degrees should have a value between 2-3 (2.5) right ?
What about the darker chamfered cut ?
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What if the light changes from a spotlight to a sunlight, does it effect the lit sides ?
Method 1. Build a maquette and use it.
Method 2. Use a 3D program to model and light the scene.
Method 3. If you want to do it without maquettes, refer to "Perspective Made Easy" by Norling, page 157. You do not need to guess, you can calculate it from the position and elevation of the light source.
The value of a plane doesn't just depend on the angle of the light rays, but also on the angle towards your eye. It is more like playing billiards, with balls coming from the light source, bouncing the plane and hitting your eye. To make things more complicating, it also depends on the plane being reflective or not.Hey guys, currently I am wondering how to calculate the degree of the side plain towards the light source (marked with the question mark). Is it correct to guess this angle by looking at the cube from the top and make a guess at the correct angle ? if so then it seems a +- 45 Degrees. If 90 degrees is full lit (0) and 0 degrees is full dark than 45 degrees should have a value between 2-3 (2.5) right ?
Grinnikend door het leven...
You are an optimist! The basic issues involved in the fall-off of illumination, and therefore of the diffuse reflection, are covered on this page:
Highlights (specular reflections) are another complication.
Why would you need this angle?
thanks for the comments guys. Some nice websites there. However, my question regarding the "degree" of the planes isn't answered yet. I am aware that you cannot assign a simple value to a plane but you can get far by knowing the degree of the plane towards the light source (and the point of view).
Imagine for instance the same box but with a different setup of lights. The height of the light sources is lower this time.
If this is correct or not, I do not know. My main question still remains on "how to measure the angle of the side plain towards the light source(s)". Since the plane is turned and the light sources are elevated (casting down) I find this hard to imagine.
Your question is not clear. Do you want to *measure*, *calculate* or *deduce from photo/rendering*. These are three different things with different set of initial parameters.
To calculate the angle of light incidence at some point on surface, you take a dot product of light direction unit vector at that point and surface normal vector at the same point. Calculating the arc cosine of that dot product will give you the incidence angle, that is, the smallest angle between the light ray and the surface. For point lights, this angle will wary even across the planar surfaces, to a degree depending on the proximity of the light source.
angle = arccos(N.L)
This is, of course, an approximation using pure lambertian diffuse lighting model.
Last edited by LaCan; August 24th, 2013 at 11:14 AM.
That is more about goniometry than about art, so you may want to try a different forum?
Grinnikend door het leven...
What do you mean ? this has everything to do with art As an artist you need to understand this, for example, lighting issue and then deduct an artistic impression of it.
so am I correct when I say that we can deduct the angle at which the light hits a surface by the normal of said surface ? The reason I want to know this is because I want to understand shading on complex forms better. An artistic guess is fine as long as it does the job.
I wouldn't say "deduce". The angle at which light hits the surface is *defined* as the angle between surface normal and light direction. I'm really not sure what are you trying to accomplish here... But if you can mentally visualize the angle between surface normal and a light ray that hits the surface, it can give you a loose hint about how bright the surface is.
For ideal diffuse reflection there's the Lambert's reflectance law. It states that reflected light intensity is proportional to the cosine of the angle between the surface normal and an incoming light ray. If you normalize incoming intensity to 0-1 range and assume that the light is white it becomes simply:
reflected_intensity = L.N = cos(angle)
It's precisely how the table posted by briggsy was calculated and precisely the way your 3d program is figuring out the brightness of various parts of your model.
However if the surface reflects specularly, you'll need to add intensity of the specular reflectance to this Lambertian equation. This is a bit trickier to calculate as it involves at least two more parameters: shininess and viewer position, and it can be expressed mathematically in several ways. The simplest is Phong/Blinn mathematical model:
specular_reflectance = pow( (2*(L.N)*N-L).V, shininess)
Where L is light direction, N is surface normal, and V is direction from the surface point to the viewer.
If there is some ambient/environment light, you'll need to add this too as a constant term.
So the complete calculation then goes as follows:
surface_brightness = ambient_reflectance + diffuse_reflectance + specular_reflectance
surface_brightness = ambient_reflectance + cos(angle) + pow( (2*(L.N)*N-L).V, shininess)
This is basically what every 3D program does when it renders a surface to which you assigned a Phong or Blinn shader. It calculates this for every pixel on the surface.
Note that visualizing diffuse reflectance is somewhat intuitive and can be used as a mental tool when rendering from imagination. Conversely, the behavior of specular reflectance and its resulting brightness is significantly harder to envision.
Last edited by LaCan; August 25th, 2013 at 06:13 PM.
this is what I want to achieve. Currently I visualize this angle using top and front/side views.But if you can mentally vis ualize the angle between surface normal and a light ray that hits the surface, it can give you a loose hint about how bright the surface is.
Very interesting, yet complicated, information (been a while since I had geometry/mathematics haha). Could you recommend a 3D program/website/app which could help me visualize lighting/shadows ? 3DSmax does not give accurate shadows for me (driver bug).
I think you're over-complicating the whole issue. Just use the broad but intuitive notion of "facing". If the surface is facing the light fully then it is fully lit. If it's facing away from light then it is completely dark. If it's facing it somewhat 45-degree-ish then it's in halftone. If it's facing the light almost fully, then it is almost fully lit. And finally, if it's facing almost away from the light, it is almost completely dark. As trivial as it sounds it gives you your 5 value steps.
Every single 3D program out there is able to do it.
Even if you have some GPU driver issues it would only affect your hardware accelerated viewports. Software-rendered image should be accurate.
What gave me trouble where skewed/rotated objects but I think have it under control now. Many thanks for your help LaCan !
The best way to develop a feel for this is to draw or paint value studies of various simple objects from life. When you observe directly from life, you know exactly where the light is and, due to stereoscopic vision, you can gauge inclination of surfaces rather accurately. It's even more effective if you keep Lambert's law in mind while practicing.
Doing such studies can help you a lot in establishing imaginary lighting situations.
Last edited by LaCan; August 25th, 2013 at 07:52 PM.