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Photography basics: Solid Angle measures
Read more: Photography basics: Solid Angle measureshttp://www.calculator.org/property.aspx?name=solid+angle
A measure of how large the object appears to an observer looking from that point. Thus. A measure for objects in the sky. Useful to retuen the size of the sun and moon… and in perspective, how much of their contribution to lighting. Solid angle can be represented in ‘angular diameter’ as well.
http://en.wikipedia.org/wiki/Solid_angle
http://www.mathsisfun.com/geometry/steradian.html
A solid angle is expressed in a dimensionless unit called a steradian (symbol: sr). By default in terms of the total celestial sphere and before atmospheric’s scattering, the Sun and the Moon subtend fractional areas of 0.000546% (Sun) and 0.000531% (Moon).
http://en.wikipedia.org/wiki/Solid_angle#Sun_and_Moon
On earth the sun is likely closer to 0.00011 solid angle after athmospheric scattering. The sun as perceived from earth has a diameter of 0.53 degrees. This is about 0.000064 solid angle.
http://www.numericana.com/answer/angles.htm
The mean angular diameter of the full moon is 2q = 0.52° (it varies with time around that average, by about 0.009°). This translates into a solid angle of 0.0000647 sr, which means that the whole night sky covers a solid angle roughly one hundred thousand times greater than the full moon.
More info
http://lcogt.net/spacebook/using-angles-describe-positions-and-apparent-sizes-objects
http://amazing-space.stsci.edu/glossary/def.php.s=topic_astronomy
Angular Size
The apparent size of an object as seen by an observer; expressed in units of degrees (of arc), arc minutes, or arc seconds. The moon, as viewed from the Earth, has an angular diameter of one-half a degree.
The angle covered by the diameter of the full moon is about 31 arcmin or 1/2°, so astronomers would say the Moon’s angular diameter is 31 arcmin, or the Moon subtends an angle of 31 arcmin.
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Convert between light exposure and intensity
Read more: Convert between light exposure and intensityimport math,sys def Exposure2Intensity(exposure): exp = float(exposure) result = math.pow(2,exp) print(result) Exposure2Intensity(0) def Intensity2Exposure(intensity): inarg = float(intensity) if inarg == 0: print("Exposure of zero intensity is undefined.") return if inarg < 1e-323: inarg = max(inarg, 1e-323) print("Exposure of negative intensities is undefined. Clamping to a very small value instead (1e-323)") result = math.log(inarg, 2) print(result) Intensity2Exposure(0.1)Why Exposure?
Exposure is a stop value that multiplies the intensity by 2 to the power of the stop. Increasing exposure by 1 results in double the amount of light.
Artists think in “stops.” Doubling or halving brightness is easy math and common in grading and look-dev.
Exposure counts doublings in whole stops:- +1 stop = ×2 brightness
- −1 stop = ×0.5 brightness
This gives perceptually even controls across both bright and dark values.
Why Intensity?
Intensity is linear.
It’s what render engines and compositors expect when:- Summing values
- Averaging pixels
- Multiplying or filtering pixel data
Use intensity when you need the actual math on pixel/light data.
Formulas (from your Python)
- Intensity from exposure: intensity = 2**exposure
- Exposure from intensity: exposure = log₂(intensity)
Guardrails:
- Intensity must be > 0 to compute exposure.
- If intensity = 0 → exposure is undefined.
- Clamp tiny values (e.g.
1e−323) before using log₂.
Use Exposure (stops) when…
- You want artist-friendly sliders (−5…+5 stops)
- Adjusting look-dev or grading in even stops
- Matching plates with quick ±1 stop tweaks
- Tweening brightness changes smoothly across ranges
Use Intensity (linear) when…
- Storing raw pixel/light values
- Multiplying textures or lights by a gain
- Performing sums, averages, and filters
- Feeding values to render engines expecting linear data
Examples
- +2 stops → 2**2 = 4.0 (×4)
- +1 stop → 2**1 = 2.0 (×2)
- 0 stop → 2**0 = 1.0 (×1)
- −1 stop → 2**(−1) = 0.5 (×0.5)
- −2 stops → 2**(−2) = 0.25 (×0.25)
- Intensity 0.1 → exposure = log₂(0.1) ≈ −3.32
Rule of thumb
Think in stops (exposure) for controls and matching.
Compute in linear (intensity) for rendering and math. -
Rendering – BRDF – Bidirectional reflectance distribution function
Read more: Rendering – BRDF – Bidirectional reflectance distribution functionhttp://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function
The bidirectional reflectance distribution function is a four-dimensional function that defines how light is reflected at an opaque surface
http://www.cs.ucla.edu/~zhu/tutorial/An_Introduction_to_BRDF-Based_Lighting.pdf
In general, when light interacts with matter, a complicated light-matter dynamic occurs. This interaction depends on the physical characteristics of the light as well as the physical composition and characteristics of the matter.
That is, some of the incident light is reflected, some of the light is transmitted, and another portion of the light is absorbed by the medium itself.
A BRDF describes how much light is reflected when light makes contact with a certain material. Similarly, a BTDF (Bi-directional Transmission Distribution Function) describes how much light is transmitted when light makes contact with a certain material
http://www.cs.princeton.edu/~smr/cs348c-97/surveypaper.html
It is difficult to establish exactly how far one should go in elaborating the surface model. A truly complete representation of the reflective behavior of a surface might take into account such phenomena as polarization, scattering, fluorescence, and phosphorescence, all of which might vary with position on the surface. Therefore, the variables in this complete function would be:
incoming and outgoing angle incoming and outgoing wavelength incoming and outgoing polarization (both linear and circular) incoming and outgoing position (which might differ due to subsurface scattering) time delay between the incoming and outgoing light ray
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Arto T. – A workflow for creating photorealistic, equirectangular 360° panoramas in ComfyUI using Flux
Read more: Arto T. – A workflow for creating photorealistic, equirectangular 360° panoramas in ComfyUI using Fluxhttps://civitai.com/models/735980/flux-equirectangular-360-panorama
https://civitai.com/models/745010?modelVersionId=833115
The trigger phrase is “equirectangular 360 degree panorama”. I would avoid saying “spherical projection” since that tends to result in non-equirectangular spherical images.
Image resolution should always be a 2:1 aspect ratio. 1024 x 512 or 1408 x 704 work quite well and were used in the training data. 2048 x 1024 also works.
I suggest using a weight of 0.5 – 1.5. If you are having issues with the image generating too flat instead of having the necessary spherical distortion, try increasing the weight above 1, though this could negatively impact small details of the image. For Flux guidance, I recommend a value of about 2.5 for realistic scenes.
8-bit output at the moment
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What is physically correct lighting all about?
Read more: What is physically correct lighting all about?http://gamedev.stackexchange.com/questions/60638/what-is-physically-correct-lighting-all-about
2012-08 Nathan Reed wrote:
Physically-based shading means leaving behind phenomenological models, like the Phong shading model, which are simply built to “look good” subjectively without being based on physics in any real way, and moving to lighting and shading models that are derived from the laws of physics and/or from actual measurements of the real world, and rigorously obey physical constraints such as energy conservation.
For example, in many older rendering systems, shading models included separate controls for specular highlights from point lights and reflection of the environment via a cubemap. You could create a shader with the specular and the reflection set to wildly different values, even though those are both instances of the same physical process. In addition, you could set the specular to any arbitrary brightness, even if it would cause the surface to reflect more energy than it actually received.
In a physically-based system, both the point light specular and the environment reflection would be controlled by the same parameter, and the system would be set up to automatically adjust the brightness of both the specular and diffuse components to maintain overall energy conservation. Moreover you would want to set the specular brightness to a realistic value for the material you’re trying to simulate, based on measurements.
Physically-based lighting or shading includes physically-based BRDFs, which are usually based on microfacet theory, and physically correct light transport, which is based on the rendering equation (although heavily approximated in the case of real-time games).
It also includes the necessary changes in the art process to make use of these features. Switching to a physically-based system can cause some upsets for artists. First of all it requires full HDR lighting with a realistic level of brightness for light sources, the sky, etc. and this can take some getting used to for the lighting artists. It also requires texture/material artists to do some things differently (particularly for specular), and they can be frustrated by the apparent loss of control (e.g. locking together the specular highlight and environment reflection as mentioned above; artists will complain about this). They will need some time and guidance to adapt to the physically-based system.
On the plus side, once artists have adapted and gained trust in the physically-based system, they usually end up liking it better, because there are fewer parameters overall (less work for them to tweak). Also, materials created in one lighting environment generally look fine in other lighting environments too. This is unlike more ad-hoc models, where a set of material parameters might look good during daytime, but it comes out ridiculously glowy at night, or something like that.
Here are some resources to look at for physically-based lighting in games:
SIGGRAPH 2013 Physically Based Shading Course, particularly the background talk by Naty Hoffman at the beginning. You can also check out the previous incarnations of this course for more resources.
Sébastien Lagarde, Adopting a physically-based shading model and Feeding a physically-based shading model
And of course, I would be remiss if I didn’t mention Physically-Based Rendering by Pharr and Humphreys, an amazing reference on this whole subject and well worth your time, although it focuses on offline rather than real-time rendering.
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