The material system is built around the alias/wavefront material format with a few extensions for accessing the advanced rendering features offered by polaris.
When polaris encounters a material without a material expression it will make a best-effort attempt to construct one by analyzing any present mtl format attributes. The following attributes of the wavefront material format are recognized by the material parser:
| Attribute | Description | Value type | Example | Notes |
|---|---|---|---|---|
| Kd | Diffuse color | Vector | Kd 0.9 0.1 0.1 |
Vector components should be in the [0, 1) range |
| Ks | Specular color | Vector | Ks 1 1 1 |
Vector components should be in the [0, 1) range |
| Tf | Transmittance color | Vector | Tf 0.9 0 0 |
Vector components should be in the [0, 1) range |
| Ke | Emissive color | Vector | Ke 10 10 10 |
No limit for emissive components |
| map_Kd | Diffuse texture | String | map_Kd "foo.jpg" |
|
| map_Ks | Specular texture | String | map_Ks "foo.png" |
|
| map_Tf | Transmittance texture | String | map_Tf "foo.tga" |
|
| map_Ke | Emissive texture | String | map_Ke "foo.exr" |
An exr/hdr file can be used for HDR rendering |
| map_bump | Bumpmap texture | String | map_bump "stones-b.png" |
|
| Ni | Refractive Index | Scalar | Ni 1.53 |
Polaris uses OpenImageIO for loading image files. This allows the renderer to parse most known image formats including openEXR and HDR/RGBE for HDR renders.
In addition to the standard mtl attributes described above, polaris also supports the following attribute extensions:
| Attribute | Description | Value type | Example | Notes |
|---|---|---|---|---|
| include | Include properties from an existing material | String | include "glass" |
This attribute can be used to extend an existing material and overwrite one or more of its attributes |
| KeScaler | Scaler value for emissive texture | Scalar | KeScaler 3.0 |
This attribute allows you to specify a 24-bit RGB emissive texture and apply a scaler to its RGB values. It's an alternative way to enable HDR rendering when exr/hdr files cannot be used |
| map_normal | Normal map texture | String | map_normal "stones-n.png" |
|
| mat_expr | Define material expression | String | mat_expr diffuse(reflectance: {0.9, 0.0}) |
See material expressions following section for more details |
When specifying a path to a texture or other external resource:
- A relative path (to the current file) can be used
- An absolute path can be used
- An http/https URL can be specified to pull the resource from a remote host
The scene compiler recognizes two reserved material names that can be defined to override global scene properties:
scene_diffuse_material: specifies the diffuse material for the scene background. If defined, this material will be sampled by rays that do not intersect any of the scene geometry. It can be used to specify a lat/lng skypbox envmap. If not defined, it defaults to a black diffuse surface.scene_emissive_material: specifies a global emissive material that simulates a directional light. By default its not used but it can be specified to enable a HDR emissive env map.
Material expressions can be used to specify layered materials, that is, materials that either use a specific BxDF surface model or combine multiple surface models using one or more operators.
Polaris uses a very simple approach to sampling layered materials. When its time to evaluate a material for a ray intersection it will traverse the layered material tree applying any operators it encounters till it hits a leaf node which is then selected as the surface material.
For more info on layered materials and how they are sampled you can skim through this very interesting presentation by Takahiro Harada.
This model simulates a smooth lambertian surface. This model supports the following parameters:
| Parameter name | Description | Type | Default | Example |
|---|---|---|---|---|
| reflectance | diffuse value | Vector OR texture | {0.2,0.2,0.2} | reflectance: {0.9,0,0} reflectance: "stones-d.jpg" |
Examples:
| Expression | Output |
|---|---|
diffuse(reflectance: {0.999, 0, 0}) |
 |
diffuse(reflectance: "stones-d.png") |
 |
This model simulates a smooth conductor. This model supports the following parameters:
| Parameter name | Description | Type | Default | Example |
|---|---|---|---|---|
| specularity | specular value | Vector OR texture | {1,1,1} | specularity: {0.9,0,0} specularity: "stones-s.jpg" |
| intIOR | internal IOR | Scalar OR mat. name | "glass" | intIOR: 1.345 intIOR: "diamond" |
| extIOR | external IOR | Scalar OR mat. name | "air" | extIOR: 1 extIOR: "air" |
Examples:
| Expression | Output |
|---|---|
conductor(intIOR: "gold", specularity: {1.0, 0.766, 0.336}) |
 |
conductor(intIOR: "silver", specularity: {0.971519, 0.959915, 0.91532}) |
 |
conductor(specularity: "checkerboard-bw.jpg") |
 |
This model simulates an ideal dielectric material where the fresnel factor is used to select whether a ray will get reflected or refracted. When rendering complex geometry using dielectrics it is advised to increase the number of ray bounces. This model supports the following parameters:
| Parameter name | Description | Type | Default | Example |
|---|---|---|---|---|
| specularity | specular value | Vector OR texture | {1,1,1} | specularity: {0.9,0,0} specularity: "stones-s.jpg" |
| transmittance | transmittance | Vector OR texture | {1,1,1} | transmittance: {0.9,0,0} transmittance: "logo-t.jpg" |
| intIOR | internal IOR | Scalar OR mat. name | "glass" | intIOR: 1.345 intIOR: "diamond" |
| extIOR | external IOR | Scalar OR mat. name | "air" | extIOR: 1 extIOR: "air" |
Examples:
| Expression | Output |
|---|---|
dielectric(intIOR: "glass") |
 |
dielectric(intIOR: "glass", specularity: {0.04, 0.04, 0.04}, transmittance: {0.5, 0, 0.9}) |
 |
dielectric(intIOR: "glass", specularity: "checkerboard-blue.jpg") |
 |
dielectric(intIOR: "glass", transmittance: "checkerboard-blue.jpg") |
 |
This model simulates a rough conductor. It uses the BRDF formula described in microfacet models for refraction through rough surfaces. This model supports the following parameters:
| Parameter name | Description | Type | Default | Example |
|---|---|---|---|---|
| specularity | specular value | Vector OR texture | {1,1,1} | specularity: {0.9,0,0} specularity: "stones-s.jpg" |
| intIOR | internal IOR | Scalar OR mat. name | "glass" | intIOR: 1.345 intIOR: "diamond" |
| extIOR | external IOR | Scalar OR mat. name | "air" | extIOR: 1 extIOR: "air" |
| roughness | roughness factor | Scalar OR texture | 0.1 | roughness: 0.5 `roughness: "stones-r.jpg" |
The following examples illustrate how the same material looks with different roughness values:
| Expression | Output |
|---|---|
roughConductor(intIOR: "gold", specularity: {1.0, 0.766, 0.336}, roughness:0.1) |
 |
roughConductor(intIOR: "gold", specularity: {1.0, 0.766, 0.336}, roughness:0.25) |
 |
roughConductor(intIOR: "gold", specularity: {1.0, 0.766, 0.336}, roughness:0.5) |
 |
roughConductor(intIOR: "gold", specularity: {1.0, 0.766, 0.336}, roughness:0.75) |
 |
This model simulates a rough dielectric material. It uses the BRDF and BTDF formulas described in microfacet models for refraction through rough surfaces as well as the fresnel factor to select between ray reflection and refraction.
This model supports the following parameters:
| Parameter name | Description | Type | Default | Example |
|---|---|---|---|---|
| specularity | specular value | Vector OR texture | {1,1,1} | specularity: {0.9,0,0} specularity: "stones-s.jpg" |
| transmittance | transmittance | Vector OR texture | {1,1,1} | transmittance: {0.9,0,0} transmittance: "logo-t.jpg" |
| intIOR | internal IOR | Scalar OR mat. name | "glass" | intIOR: 1.345 intIOR: "diamond" |
| extIOR | external IOR | Scalar OR mat. name | "air" | extIOR: 1 extIOR: "air" |
| roughness | roughness factor | Scalar OR texture | 0.1 | roughness: 0.5 roughness: "stones-r.jpg" |
| Expression | Output |
|---|---|
roughDielectric(intIOR: "glass", specularity: {0.9, 0.9, 0.9}, roughness: 0.2) |
 |
roughDielectric(intIOR: "glass", roughness: "earth-r.jpg") |
 |
This model describes a surface that emits light. It supports the following parameters:
| Parameter name | Description | Type | Default | Example |
|---|---|---|---|---|
| radiance | emitted radiance value | Vector OR texture | {1,1,1} | radiance: {5,5,5} radiance: "spot.jpg" |
Operators are special functions that either modify or combine their operands. Their operands are either another nested operator or a bxdf surface definition. In addition, expression operands may also reference other materials by name. For example:
newmtl gold
mat_expr conductor(intIOR: "gold", specularity: {1.0, 0.766, 0.336})
newmtl silver
mat_expr conductor(intIOR: "silver", specularity: {0.971519, 0.959915, 0.915324})
newmtl weird
mat_expr mixMap("gold", "silver", "checkerboard-bw.jpg")The mix operator accepts two expression operands A and B and a weight W in the [0,1]
range.
When sampling this operator, a random value is used to select either
A or B based on the weights (A chosen with probablity W and B chosen
with probability 1-W).
Examples:
| Example | Output |
|---|---|
mix(diffuse(reflectance: {0.999,0,0}), diffuse(reflectance: {0,0,0.999}), 0.5) |
 |
mix(diffuse(reflectance: "stones-d.jpg"), conductor(intIOR: "silver", specularity: {0.971519, 0.959915, 0.91532}), 0.6) |
 |
The mix operator accepts two expression operands A and B and a single channel texture
containing a per-pixel sampling weight.
When sampling this operator, the weight W is sampled from the weight texture
using the UV coordinates of the surface intersection and a random value is used
to select either A or B based on the weights (A chosen with probablity
W and B chosen with probability 1-W).
Examples:
| Example | Output |
|---|---|
mix(conductor(intIOR: "gold", specularity: {1.0, 0.766, 0.336)), conductor(intIOR: "silver", specularity: {0.971519, 0.959915, 0.91532}), 0.6), "checkerboard-bw.jpg") |
 |
This is a pass-through operator that modifies the normal of the surface intersection point using an image. It accepts an expression operand and a texture argument.
Bump maps are single-channel grayscale images and polaris needs to reconstruct the bi-tangent vectors from by fetching 3 samples from the bumpmap texture. It is usually faster to use a normal map instead.
| Example | Bump map | Output |
|---|---|---|
bumpMap(diffuse(reflectance: "stones-d.png"), "stones-b.png") |
 |
 |
This is a pass-through operator that modifies the normal of the surface intersection point using an image. It accepts an expression operand and a texture argument.
Normal maps are RGB images where each component specifies an offset for the X, Y and ~ coordinates. This operator achieves the same result as the bumpMap operator but it is a bit faster to evaluate.
| Example | Normal map | Output |
|---|---|---|
normalMap(diffuse(reflectance: "stones-n.png"), "stones-b.png") |
 |
 |
The disperse operator is used to simulate light dispersion inside dielectric materials where essentially, rays exhibit a slightly different IOR based on their wavelength.
This operator accepts an expression operand and two vectors (one for the internal
and one for the external IOR) with IOR values for the R, G and B channels. Unless
rendering a scene where light passes through dielectric materials (eg. glass filled with water),
the extIOR vector can be set to {0,0,0} which effectively makes polaris ignore it
and just use whatever value the leaf node defines for extIOR.
A correct approximation of dispersion would require a tracer capable of performing spectral rendering. Polaris simulates dispersion using different IORs for the R, G and B channels.
Whenever the dispersion operator is evaluated, we first check the path flags to detect whether some ray has undergone dispersion somewhere along the path. If this is the first time that the path will get dispersed then we randomly select a channel, update the path flags to reflect the selected channel and force the appropriate int/ext IORs to the leaf node. If we detect a prior dispersion event, we lookup the path flags to select the appropriate int/ext IOR values based on the previously selected channel.
In both cases, the disperse operator will setup a tint value to act as a color filter for the selected R, G or B channel. Due to the way that polaris approximates dispersion, the sample count needs to be effectively tripled to get a correct image.
| Example | Output |
|---|---|
disperse(dielectric(intIOR: "diamond"), intIOR: {2.40,2.43,2.46}, extIOR: {0,0,0}) |
 |
The following tables (obtained here) contain a list of specularity values for dielectrics and common metals. It is important to note that dielectrics have monochromatic specularity values whereas metals have RGB specularity values.
| Dielectric | Specularity |
|---|---|
| Quartz | {0.045593921, 0.045593921, 0.045593921} |
| Ice | {0.017908907, 0.017908907, 0.017908907} |
| Water | {0.020373188, 0.020373188, 0.020373188} |
| Alcohol | {0.01995505, 0.01995505, 0.01995505} |
| Glass | {0.04, 0.04, 0.04} |
| Milk | {0.022181983, 0.022181983, 0.022181983} |
| Ruby | {0.077271957, 0.077271957, 0.077271957} |
| Crystal | {0.111111111, 0.111111111, 0.111111111} |
| Diamond | {0.171968833, 0.171968833, 0.171968833} |
| Skin | {0.028, 0.028, 0.028} |
| Metal | Specularity |
|---|---|
| Silver | { 0.971519, 0.959915, 0.915324} |
| Aluminium | { 0.913183, 0.921494, 0.924524} |
| Gold | { 1, 0.765557, 0.336057} |
| Copper | { 0.955008, 0.637427, 0.538163} |
| Chromium | { 0.549585, 0.556114, 0.554256} |
| Nickel | { 0.659777, 0.608679, 0.525649} |
| Titanium | { 0.541931, 0.496791, 0.449419} |
| Cobalt | { 0.662124, 0.654864, 0.633732} |
| Platinum | { 0.672411, 0.637331, 0.585456} |
The following table summarizes the list of built-in IOR values that can be referenced by name for BxDF models that require an IOR value.
Note that material names are case-insensitive. Here is an example how to reference material IORs by name:
dielectric(intIOR: "glass", extIOR: "air")| Material name | IOR |
|---|---|
| Acetone | 1.36 |
| Actinolite | 1.618 |
| Agalmatoite | 1.550 |
| Agate | 1.544 |
| Agate, Moss | 1.540 |
| Air | 1.0002926 |
| Alcohol | 1.329 |
| Alexandrite | 1.745 |
| Aluminum | 1.44 |
| Amber | 1.546 |
| Amblygonite | 1.611 |
| Amethyst | 1.544 |
| Anatase | 2.490 |
| Andalusite | 1.641 |
| Anhydrite | 1.571 |
| Apatite | 1.632 |
| Apophyllite | 1.536 |
| Aquamarine | 1.577 |
| Aragonite | 1.530 |
| Argon | 1.000281 |
| Asphalt | 1.635 |
| Augelite | 1.574 |
| Axinite | 1.675 |
| Azurite | 1.730 |
| Barite | 1.636 |
| Barytocalcite | 1.684 |
| Benitoite | 1.757 |
| Benzene | 1.501 |
| Beryl | 1.577 |
| Beryllonite | 1.553 |
| Brazilianite | 1.603 |
| Bromine (liq) | 1.661 |
| Bronze | 1.18 |
| Brownite | 1.567 |
| Calcite | 1.486 |
| Calspar | 1.486 |
| Cancrinite | 1.491 |
| Carbon Dioxide (gas) | 1.000449 |
| Carbon Disulfide | 1.628 |
| Carbon Tetrachloride | 1.460 |
| Cassiterite | 1.997 |
| Celestite | 1.622 |
| Cerussite | 1.804 |
| Ceylanite | 1.770 |
| Chalcedony | 1.530 |
| Chalk | 1.510 |
| Chalybite | 1.630 |
| Chrome Green | 2.4 |
| Chrome Red | 2.42 |
| Chrome Yellow | 2.31 |
| Chromium | 2.97 |
| Chrysoberyl | 1.745 |
| Chrysocolla | 1.500 |
| Chrysoprase | 1.534 |
| Citrine | 1.550 |
| Clinozoisite | 1.724 |
| Cobalt Blue | 1.74 |
| Cobalt Green | 1.97 |
| Cobalt Violet | 1.71 |
| Colemanite | 1.586 |
| Copper | 1.10 |
| Copper Oxide | 2.705 |
| Coral | 1.486 |
| Cordierite | 1.540 |
| Corundum | 1.766 |
| Crocoite | 2.310 |
| Crystal | 2.00 |
| Cuprite | 2.850 |
| Danburite | 1.633 |
| Diamond | 2.417 |
| Diopside | 1.680 |
| Dolomite | 1.503 |
| Dumortierite | 1.686 |
| Ebonite | 1.66 |
| Ekanite | 1.600 |
| Elaeolite | 1.532 |
| Emerald | 1.576 |
| Emerald, Synth flux | 1.561 |
| Emerald, Synth hydro | 1.568 |
| Enstatite | 1.663 |
| Epidote | 1.733 |
| Ethanol | 1.36 |
| Ethyl Alcohol | 1.36 |
| Euclase | 1.652 |
| Fabulite | 2.409 |
| Feldspar, Adventurine | 1.532 |
| Feldspar, Albite | 1.525 |
| Feldspar, Amazonite | 1.525 |
| Feldspar, Labradorite | 1.565 |
| Feldspar, Microcline | 1.525 |
| Feldspar, Oligoclase | 1.539 |
| Feldspar, Orthoclase | 1.525 |
| Fluoride | 1.56 |
| Fluorite | 1.434 |
| Formica | 1.47 |
| Garnet, Almandine | 1.760 |
| Garnet, Almandite | 1.790 |
| Garnet, Andradite | 1.820 |
| Garnet, Demantoid | 1.880 |
| Garnet, Grossular | 1.738 |
| Garnet, Hessonite | 1.745 |
| Garnet, Rhodolite | 1.760 |
| Garnet, Spessartite | 1.810 |
| Gaylussite | 1.517 |
| Glass | 1.51714 |
| Glass, Albite | 1.4890 |
| Glass, Crown | 1.520 |
| Glass, Crown, Zinc | 1.517 |
| Glass, Flint, Dense | 1.66 |
| Glass, Flint, Heaviest | 1.89 |
| Glass, Flint, Heavy | 1.65548 |
| Glass, Flint, Lanthanum | 1.80 |
| Glass, Flint, Light | 1.58038 |
| Glass, Flint, Medium | 1.62725 |
| Glycerine | 1.473 |
| Gold | 0.47 |
| Hambergite | 1.559 |
| Hauynite | 1.502 |
| Helium | 1.000036 |
| Hematite | 2.940 |
| Hemimorphite | 1.614 |
| Hiddenite | 1.655 |
| Howlite | 1.586 |
| Hypersthene | 1.670 |
| Ice | 1.309 |
| Idocrase | 1.713 |
| Iodine Crystal | 3.34 |
| Iolite | 1.548 |
| Iron | 1.51 |
| Ivory | 1.540 |
| Jade, Nephrite | 1.610 |
| Jadeite | 1.665 |
| Jasper | 1.540 |
| Jet | 1.660 |
| Kornerupine | 1.665 |
| Kunzite | 1.655 |
| Kyanite | 1.715 |
| Lapis Gem | 1.500 |
| Lapis Lazuli | 1.61 |
| Lazulite | 1.615 |
| Lead | 2.01 |
| Leucite | 1.509 |
| Magnesite | 1.515 |
| Malachite | 1.655 |
| Meerschaum | 1.530 |
| Mercury (liq) | 1.62 |
| Methanol | 1.329 |
| Moldavite | 1.500 |
| Moonstone, Adularia | 1.525 |
| Moonstone, Albite | 1.535 |
| Natrolite | 1.480 |
| Nephrite | 1.600 |
| Nitrogen (gas) | 1.000297 |
| Nitrogen (liq) | 1.2053 |
| Nylon | 1.53 |
| Obsidian | 1.489 |
| Olivine | 1.670 |
| Onyx | 1.486 |
| Opal | 1.450 |
| Oxygen (gas) | 1.000276 |
| Oxygen (liq) | 1.221 |
| Painite | 1.787 |
| Pearl | 1.530 |
| Periclase | 1.740 |
| Peridot | 1.654 |
| Peristerite | 1.525 |
| Petalite | 1.502 |
| Phenakite | 1.650 |
| Phosgenite | 2.117 |
| Plastic | 1.460 |
| Plexiglas | 1.50 |
| Polystyrene | 1.55 |
| Prase | 1.540 |
| Prasiolite | 1.540 |
| Prehnite | 1.610 |
| Proustite | 2.790 |
| Purpurite | 1.840 |
| Pyrite | 1.810 |
| Pyrope | 1.740 |
| Quartz | 1.544 |
| Quartz, Fused | 1.45843 |
| Rhodizite | 1.690 |
| Rhodochrisite | 1.600 |
| Rhodonite | 1.735 |
| Rock Salt | 1.544 |
| Rubber, Natural | 1.5191 |
| Ruby | 1.760 |
| Rutile | 2.62 |
| Sanidine | 1.522 |
| Sapphire | 1.760 |
| Scapolite | 1.540 |
| Scapolite, Yellow | 1.555 |
| Scheelite | 1.920 |
| Selenium, Amorphous | 2.92 |
| Serpentine | 1.560 |
| Shell | 1.530 |
| Silicon | 4.24 |
| Sillimanite | 1.658 |
| Silver | 0.18 |
| Sinhalite | 1.699 |
| Smaragdite | 1.608 |
| Smithsonite | 1.621 |
| Sodalite | 1.483 |
| Sodium Chloride | 1.544 |
| Sphalerite | 2.368 |
| Sphene | 1.885 |
| Spinel | 1.712 |
| Spodumene | 1.650 |
| Staurolite | 1.739 |
| Steatite | 1.539 |
| Steel | 2.50 |
| Stichtite | 1.520 |
| Strontium Titanate | 2.410 |
| Styrofoam | 1.595 |
| Sulphur | 1.960 |
| Synthetic Spinel | 1.730 |
| Taaffeite | 1.720 |
| Tantalite | 2.240 |
| Tanzanite | 1.691 |
| Teflon | 1.35 |
| Thomsonite | 1.530 |
| Tiger eye | 1.544 |
| Topaz | 1.620 |
| Topaz, Blue | 1.610 |
| Topaz, Pink | 1.620 |
| Topaz, White | 1.630 |
| Topaz, Yellow | 1.620 |
| Tourmaline | 1.624 |
| Tremolite | 1.600 |
| Tugtupite | 1.496 |
| Turpentine | 1.472 |
| Turquoise | 1.610 |
| Ulexite | 1.490 |
| Uvarovite | 1.870 |
| Variscite | 1.550 |
| Vivianite | 1.580 |
| Wardite | 1.590 |
| Water | 1.33157 |
| Willemite | 1.690 |
| Witherite | 1.532 |
| Wulfenite | 2.300 |
| Zincite | 2.010 |
| Zircon, High | 1.960 |
| Zircon, Low | 1.800 |
| Zirconia, Cubic | 2.170 |
The mitsuba model used in the example renderings was obtained from McGuire2011.