Materials across lights and observers
An observing condition (hereafter "condition") is an observer (having a set of sensors) under a light. A material's reflectance gives its measurement in any condition, and each measurement turns into Wpt and WLab through that condition's Wpt normalization. For most materials the result barely moves from condition to condition; how far and which way it does move is the material's own behavior. Measured in many conditions, one material makes a small cloud of points, its Wpt shift manifold. Choose the materials and the lights and observers, and see each material's cloud and how pairs compare in every condition.
1. The materials
Names are optional. Any wavelength grid covering at least 420 to 680 nm; values from 0 to 1, or percent. Changing the layout rewrites what is in the box.
The materials in use
Each reflectance given above, and any copies of it. Copy a material, then scale or shift the copy: scaling multiplies its reflectance at every wavelength, shifting adds the same amount at every wavelength (never going below 0). Materials made this way from one reflectance belong to one spectral hue plane. Scaling a reflectance scales its Wpt shifts by the same factor, so its shift manifold keeps its shape and only its size changes; shifting it adds the same Wpt in every condition (white is W = 100, p = t = 0 in all of them), so its Wpt shifts do not change at all. WLab is not linear, so its shifts change a little in both cases.
2. The lights and observers
The lights and observers are the observing conditions each material is seen in: every light with every observer. Together they stand for the spread of everyday viewing that a material's color shifts across; more lights or more varied observers widen the clouds, and a single light or observer shows what that one alone does.
Lights
Your light: wavelength in nm and relative power, any scale.
Observers
Your observer: wavelength in nm, then three or more sensitivity curves, any scale.
ICC (version 2 or 4) or iccMAX (version 5) profiles, binary (.icc) or as XML. Each gives one observer and one light, used where chosen above: those of its spectral viewing conditions tag (or that of the version 5 profile inside a hybrid profile), or CIE 1931 (2°) and D50, the standard PCS, for a profile without them, as every version 2 or 4 profile.
The reference condition
The shifts are measured from the reference condition. WLab's own reference is CIE 1931 under illuminant C; under a light in everyday use, such as D65, the shifts read as "compared with daylight".
3. How far each material moves
ΔEWLab from the reference: the WLab difference between the material in each condition and the same material in the reference condition. Small for most materials; larger for those whose color depends more on the light and the observer (color inconstancy). The chips show each material in the reference condition, as the display color (sRGB) of its WLab, clipped where outside sRGB.
Where the shifts go: each WLab shift split into a change in lightness (ΔLw), a change in chroma (ΔC′, along the material's own chroma direction in the reference condition: more or less colorful) and a change in hue (ΔH′, across it). The three are at right angles, so ΔLw² + ΔC′² + ΔH′² = ΔEWLab² in every condition, and the columns give each one's share of ΔEWLab² over all the conditions; they add to 100%. A material whose color is inconstant mostly in hue shows a large hue share. A gray, or a metamer of one, has no chroma in the reference and so no direction to tell chroma from hue: the two are given together. The split is made in WLab, not Wpt, because WLab is the one meant to space differences evenly.
4. Waypoint shift manifolds
In Wpt and WLab, a direction means different things for different materials: for a blue, a shift toward +bw is mostly a loss of chroma; for a green, the same shift is mostly a change of hue. Turned to each material's hue, every manifold has the same directions: ΔH′ is a change of hue toward a larger hue angle, ΔC′ is more chroma, and ΔLw is up. Turning keeps each manifold's shape and size; only the way it faces changes.
Turning one view turns them all. Each view on its own scale shows the shapes: the materials of one spectral hue plane (one reflectance scaled and shifted) make the same shape. The same scale in every view shows how large each manifold is.
The shifts in three dimensions
Drag to turn the view (or focus it and use the arrow keys). Each point is one condition: the material's shift from the reference. Lightness (W or Lw) is up.
The shifts seen from above
5. Pairs, condition by condition
How large the differences are, over the conditions
How to read it: ΔEWLab between the two materials, condition by condition. In the reference is how far apart the pair is in the reference condition; 0.00 means the two match, or they are metameric, for that condition. Mean, median, smallest and largest sum up the same difference over the other conditions. A small largest value means the pair stays together in all of them. A median well below the mean means most conditions keep the pair close and a few take it far apart; the histogram shows those few as a tail to the right, and where it is largest names the worst. A smallest of 0.00 means there is a condition where the pair matches or is metameric; where it is smallest names the first such condition and how many others there are (hover for which): every condition when the two spectra are the same. Each example's second material was made to match the first in one condition (D50 for the reds, D65 for the PMCC twins, the reference for the grays), so the other values show how well a match made in one condition holds up in the rest. With one light and one observer chosen beside the reference, the table is a simple index of metamerism: a pair that matches in the reference condition, and how far apart it is in the other.
What each pair has in common
How to read it: each column asks a question about the pair, and its number answers it: 0 when the answer is yes. Numbers, not verdicts: how close to 0 counts as yes is left to you. The first two numbers are spectral: root mean squares over the 81 wavelengths from 380 to 780 nm in steps of 5 nm, all weighted alike, with no light and no observer. Reflectances run from 0 to 1, so 0.01 is 1 percent of reflectance. The next two are in Wpt, over the reference and the conditions chosen above. A dotted underline means more on hover. In the brand red example, submission 1 leaves 0.0129 of its reflectance, 33% of its shifts and 2.25° of hue: nearer to a copy of the standard. Submission 2 leaves 0.0749, 90% and 26.69°: it is not.
- Is the second a scaled and shifted copy of the first? The second is fitted as a × the first + b (a and b on hover), and the number is the spectral RMS of what the fit leaves over. 0 means the two belong to one spectral hue plane, as in the plane example; then they also shift alike and keep the same hue. A dash means the first is flat (a gray): any copy of it is flat too, so the next column answers the question.
- Do they differ only in W? The difference spectrum, second − first, wavelength by wavelength, and its spectral RMS about its own mean (the mean on hover). 0 means the difference is flat: the second is higher or lower in W by 100 × the mean, by the same amount in every condition, and the two never differ in hue. The more uneven the difference, the further the pair can come apart as the condition changes.
- Do they shift alike? The second's Wpt shifts fitted as k times the first's, condition by condition (k on hover), and the share of them the fit leaves over, from 0% to 100%. 0% means the two move the same way from condition to condition, the second k times as far; for one spectral hue, k = a. Near 100% means they shift in unrelated ways. A dash means the first (a gray) does not shift.
- Do they keep the same hue? The largest difference between the two Wpt hue angles, over the reference and every condition. It is 0° for one spectral hue. A pair that matches in one condition and turns different hues in others shows it here. A dash means a gray is in the pair: it has no hue angle.
- Where do they match? The conditions where ΔEWLab between the two is 0.00 to two decimals (hover for which). There the two are metameric, and their difference spectrum is a metameric black for that condition. The reference is counted once, also when it is one of the conditions chosen above.
The pairs' difference manifolds
Each pair's two shift manifolds, one color each, in the coordinates chosen in section 4 (turned to the hue, both are turned to the first material's), with a line joining the pair's two points in each condition. Each line is how the pair's difference has shifted from the reference. In Wpt, which is linear, it is the Wpt shift of the difference spectrum, second − first, and the lines together are the pair's difference manifold; in WLab, which is not, the lines are close to that but not exactly it. In Wpt, a pair of one spectral hue has its lines on rays through the origin (the second's shifts are a times the first's), and a pair that differs only in W has lines of length 0; in WLab both hold only roughly. For a gray and a metamer of it, the lines start at the origin in any coordinates (the gray does not shift). The pair's ΔEWLab depends also on where the pair is, not only on these lines.