Fading a group of overlapping shapes is not generally the same as fading every shape separately. In a group fade, the shapes are first combined into one appearance and that result is made translucent. In an individual fade, each shape becomes translucent before the overlaps are combined. Previously hidden lower shapes can then contribute inside the overlap.
This guide extends The Gold Standard of Visual Arts into a practical digital-making question. It uses original shape exercises and explicitly defined compositing mathematics. The aim is to help a learner predict, observe and explain a visual change, then choose the treatment that serves the artwork. The calculations describe a controlled model rather than every application’s defaults or the behaviour of physical paint.
eduKateSG · Visual Arts
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Choose the question closest to your task, or follow the chapters in order. Each route leads into the complete worked explanation.
ROUTE 1 · CHAPTERS 1–4
Define the visual intention
Set up a controlled overlap and a consistent colour model.
ROUTE 3 · CHAPTERS 9–12
Follow the mathematics
Track ordering, premultiplied contributions and partial transparency.
ROUTE 5 · CHAPTERS 17–21
Check the finished work
Preserve editable work, inspect edges and attempt a changed-opacity task.
Chapter contents
Define the visual intention · Chapters 1–4
1. Start with the visual intention
2. Define the controlled comparison
Compare the two fades · Chapters 5–8
5. Calculate the group fade at an overlap
6. Calculate the individual fades in order
Follow the mathematics · Chapters 9–12
9. Explain why reversing the shapes changes one result
10. Follow the premultiplied representation carefully
Choose the operation · Chapters 13–16
13. Do not expect one individual setting to fix every region
14. Treat pass-through and isolation as part of the setup
Check the finished work · Chapters 17–21
17. Read soft edges as partial contributions
18. Attempt a changed-opacity transfer
19. Build a practical making and critique check
20. Questions about fading groups and overlapping shapes
21. Continue through visual making, colour and source routes
Mira has drawn a small emblem from a blue circle and an overlapping red triangle. At full opacity, the triangle covers part of the circle. She wants the complete emblem to become quieter against the page while retaining its internal arrangement. She reduces each shape to fifty per cent opacity and notices blue appearing through the triangle.
The new result may be attractive, but it is a different visual decision. The shapes now read more like overlapping translucent pieces. If the intention was to fade the finished emblem as one object, changing each component’s opacity has altered more than its overall prominence.
Begin by naming the desired relationship. Should the upper shape continue to conceal the lower one inside the emblem? Should their overlap become visible as a separate region? Should the background show through the complete object? These questions distinguish several possible outcomes before a slider is moved.
The gold standard is a purposeful choice supported by observation. There is no universal rule that a group fade is more artistic or that individual transparency is a mistake. The problem arises when a learner expects one operation to preserve a relationship that it actually changes. A short controlled comparison can make the difference clear enough to use in illustration, diagrams, lettering, animation and other visual work.
For the main examples, use two flat shapes, ordinary source-over compositing and one opaque background. The lower shape is blue, the upper shape red. They are fully opaque before the fade. No blend mode, filter, texture, mask, lighting effect or colour adjustment is added.
At a sample point where they overlap completely, the red upper shape hides the blue lower shape at full opacity. At a point covered only by the blue shape, blue is visible. At a point outside both shapes, only the background appears. These three sample locations make the comparison easier to diagnose than looking at the whole composition at once.
A group fade means first combining the shapes against transparency into their normal full-opacity group appearance, then applying one group opacity g. An individual fade means applying opacity g to each shape before combining them. These are the two operations being compared throughout the main worked example.
Applications may offer isolated groups, pass-through groups and other settings. Do not assume a folder icon establishes the exact mathematical operation. The Krita manual's group-layer explanation describes combining a group’s layers before using the intermediate result outside, and notes pass-through behaviour. Use the relevant application’s verified documentation and a small test when matching this lesson to an actual file.
CHAPTER 3 OF 21 · Define the visual intention
3. Keep colour coordinates separate from appearance
The numerical examples use RGB coordinates from zero to one in a specified linear-light working model. Red is R = (1, 0, 0), blue is B = (0, 0, 1), white is W = (1, 1, 1) and black is (0, 0, 0). These are mathematical coordinates, not promises that an exported image will store those exact displayed code values.
Display encodings, colour management and compositing spaces matter when reproducing numerical results in software. A midpoint of encoded channel numbers need not correspond to a midpoint in linear light. Keep the working representation fixed when comparing the two fade operations, so a second difference is not mixed into the exercise.
The existing guide to colour spaces, gamma correction and digital displays develops that separate representation question. Here, the main question is where opacity is applied in the sequence of combining shapes. A consistent representation lets us isolate it.
A student can understand the visual relationship without calculating channel values. The calculations provide a reproducible check for readers who want to test their explanation. First predict whether the lower shape can contribute inside the overlap. Then calculate or inspect the controlled result. The numbers should clarify the observed structure rather than replace looking at the artwork.
CHAPTER 4 OF 21 · Define the visual intention
4. Read opacity through one source-over operation
For a foreground colour S with opacity a over an opaque background C, the model result is aS + (1 − a)C. At a = 1, the foreground completely determines the sample. At a = 0, only the background remains. At a = 0.5, both have equal weights in the chosen coordinates.
Place a red shape at opacity 0.5 over white. The result is 0.5(1, 0, 0) + 0.5(1, 1, 1) = (1, 0.5, 0.5). Place a blue shape at the same opacity over white and obtain (0.5, 0.5, 1). Each result is one foreground-background combination.
The W3C Compositing and Blending specification supplies the source-over framework used for the model. The mathematical examples below are original applications of that framework. They assume normal source-over, rather than a mode such as Multiply or Screen.
A common shortcut says that fifty per cent opacity simply makes a colour fifty per cent lighter. The formula shows why that wording is incomplete. The result depends on the backdrop. Red over white and red over black move toward different colours. Opacity determines contributions to a combination; it is not a universal lightness adjustment independent of what lies beneath.
At the full-overlap sample, the opaque upper red shape completely hides the lower blue shape inside the unfaded group. The group’s local colour is therefore red, with alpha one. Applying group opacity g = 0.5 makes that completed local result half opaque.
Composite the group over white: 0.5R + 0.5W = (1, 0.5, 0.5). The lower blue shape remains concealed by the upper red shape within the group’s internal appearance. White enters because the completed group is translucent against its external background.
This is the relationship Mira originally intended: preserve the emblem’s internal occlusion while reducing its prominence as a whole. At a blue-only sample, the group yields half blue over white. At an outside sample, nothing changes. The opacity is applied to the finished group appearance at every location.
Ask the learner to explain why blue contributes nothing at the overlap in this example. The reason is not that blue was deleted or switched off. It was hidden by the opaque red shape when the group’s internal image was formed. Making that image translucent afterward does not reverse the already-completed internal occlusion. The sequence of operations determines which information remains visible in the intermediate image.
Now apply opacity 0.5 to each shape before compositing. First place the lower blue shape over white. Its result is 0.5B + 0.5W = (0.5, 0.5, 1). This becomes the backdrop for the red upper shape.
Next place half-opacity red over that result: 0.5R + 0.5(0.5B + 0.5W). Expanding gives 0.5R + 0.25B + 0.25W = (0.75, 0.25, 0.5). Blue now contributes because the upper red shape was made translucent before the overlap was combined.
| Sample in the controlled emblem | Group opacity 0.5 | Each shape opacity 0.5 |
|---|---|---|
| Red-over-blue overlap on white | 0.5R + 0.5W = (1, 0.5, 0.5) | 0.5R + 0.25B + 0.25W = (0.75, 0.25, 0.5) |
| Blue-only area on white | (0.5, 0.5, 1) | (0.5, 0.5, 1) |
| Red-only area on white | (1, 0.5, 0.5) | (1, 0.5, 0.5) |
| Outside both shapes | White | White |
The single-shape areas match while the overlap differs. That pattern is a useful diagnostic. It explains why a learner may initially think the two methods agree, then notice an unexpected seam only where shapes intersect. Compare the overlap deliberately instead of judging equivalence from one isolated part of the design.
The individual-fade result contains white with weight 0.25, rather than 0.50. Each translucent shape partly covers the remaining background contribution. Two half-opacity shapes therefore do not leave half of the original backdrop in a full overlap under this model.
For n fully overlapping opaque shapes each faded to the same individual opacity g, the surviving background weight is (1 − g)^n. The effective combined alpha is 1 − (1 − g)^n. This formula concerns the stack’s opacity; the output colour still depends on the shapes’ colours and ordering.
With g = 0.5, two shapes produce effective alpha 0.75, three produce 0.875 and four produce 0.9375. A group made from the corresponding full-opacity stack and faded once to 0.5 instead has alpha 0.5 at such a sample. More overlapping components can therefore change the difference substantially.
This is useful for diagnosing dense overlaps in a diagram or decorative pattern. If every component is independently faded, regions with more stacked shapes can become more opaque than regions with fewer. That may be the desired visual rhythm. If the intention is a uniformly faded silhouette, it may be an unwanted structural change. The appropriate choice follows the intended relationship, then a controlled check of the actual overlap pattern.
CHAPTER 8 OF 21 · Compare the two fades
8. Use identical black shapes to isolate opacity
Different colours can make the first example feel like a colour-mixing problem. Repeat it with two identical opaque black shapes on white. At the overlap, a group fade of 0.5 produces 0.5 black plus 0.5 white, or coordinate (0.5, 0.5, 0.5).
Fading each black shape to 0.5 yields effective alpha 0.75. The result over white is (0.25, 0.25, 0.25). In the chosen linear-light coordinates, the overlap is darker because less white contributes. The difference remains even though both shape colours are identical.
At a sample occupied by only one black shape, both treatments give (0.5, 0.5, 0.5). The individual treatment therefore creates a darker internal overlap, while the group treatment preserves a single flat faded silhouette. This is a particularly clear exercise for lettering or an emblem assembled from overlapping pieces.
Do not interpret the coordinate 0.5 as a universal perceptual halfway grey or an exact encoded screen value. The representation was defined earlier. The lesson is the difference in contributions. A paper prediction, a controlled digital test and a clear explanation of the overlap are enough to establish it without requiring a claim about how every display renders the same numerical triplet.
CHAPTER 9 OF 21 · Follow the mathematics
9. Explain why reversing the shapes changes one result
Reverse the main emblem so blue lies above red. With a group fade, the overlap becomes half blue over white: (0.5, 0.5, 1). With individual fades, it becomes 0.5B + 0.25R + 0.25W = (0.5, 0.25, 0.75).
In both cases, reversing the stack changes the result because the upper shape has a different colour. The group result still preserves the full-opacity internal occlusion. The individual result allows the lower shape to contribute through the upper one. The two questions, layer order and location of the fade, must both be specified.
An unlabelled screenshot cannot reliably establish either operation. Record which shape is above, which opacity changed and which group or isolation setting was used. Otherwise, two visually different results might be compared as though they differed in only one factor when several factors changed.
The existing Digital Painting guide on deliberate pixels, editable layers and reliable exports introduces opacity and layer order. This exercise extends that foundation by comparing two stages at which opacity can act. Keep the original simple shape test available when moving to a more complex painting, where many simultaneous changes can conceal the cause.
CHAPTER 10 OF 21 · Follow the mathematics
10. Follow the premultiplied representation carefully
For transparent intermediate results, colour and alpha need to be carried together. Let a shape have straight colour C and alpha a. Its premultiplied colour is p = aC. Under normal source-over, source pS over backdrop pB produces pOut = pS + (1 − aS)pB, with alpha aOut = aS + (1 − aS)aB.
Applying a group fade factor g to a completed transparent group multiplies both its premultiplied colour and its alpha by g. Multiplying alpha alone while leaving premultiplied colour unchanged does not represent the same fade. The representation and operation must agree.
These equations are the bookkeeping behind the simpler opaque-background examples. They keep intermediate contributions available until the group is placed over its external backdrop. When output alpha is positive, dividing the premultiplied colour by alpha recovers a straight colour representation. At alpha zero, that division is undefined and unnecessary for displaying the fully transparent sample.
A visual arts learner does not need to memorise every symbol. The practical takeaway is that transparency is carried with the intermediate image. A group fade applies to that combined image, while individual fades modify the components before combination. The mathematical representation helps explain why two operations with the same slider value can preserve different visible relationships.
CHAPTER 11 OF 21 · Follow the mathematics
11. Generalise to partially transparent components
Let the lower component have straight colour A and original alpha a, and the upper component have straight colour B and original alpha b. Both alphas lie from zero to one. Before any additional fade, the combined premultiplied colour is p = bB + (1 − b)aA, and its alpha is b + (1 − b)a.
A group fade gives pGroup = g[bB + (1 − b)aA]. Fading both components individually gives pIndividual = gbB + (1 − gb)gaA. Subtracting the two gives pIndividual − pGroup = g(1 − g)abA. The alpha difference is g(1 − g)ab.
Over an opaque external backdrop C, the final colour difference becomes g(1 − g)ab(A − C). The backdrop term matters: comparing only premultiplied colours without their alphas would miss part of the final visible result.
This formula identifies the lower component as the source of the newly revealed contribution relative to the backdrop. It also shows why overlap and intermediate opacity matter. The factor vanishes when either component has zero alpha or when g is zero or one. The derivation is for normal source-over in the defined model, not for arbitrary blend modes. Use it to explain a controlled example rather than force every application effect into the same expression.
CHAPTER 12 OF 21 · Follow the mathematics
12. Identify when the treatments can agree
The operations agree at points where only one component contributes, under the main model. They also agree when no additional fading occurs, g = 1, or when the entire result is made fully transparent, g = 0. These cases are useful checks on the general formula.
A particular opaque backdrop can also hide a difference. If the lower colour A equals that backdrop C, the final colour difference g(1 − g)ab(A − C) is zero there even though the intermediate alphas may differ. Agreement on one background therefore does not necessarily establish that two transparent results are equivalent on every background.
Do not use an easy matching case to prove a general identity. Two non-overlapping shapes at fifty per cent will match locally under both treatments; that does not tell us what happens once they overlap. Likewise, a black lower shape on a black backdrop can conceal a difference that becomes visible on white.
A good evidence check deliberately includes a full overlap, a single-shape area and contrasting backgrounds. The aim is not to hunt for defects in a finished artwork. It is to test the specific claim that two operations preserve the same appearance. Choose samples that could reveal a difference before declaring the treatments interchangeable.
CHAPTER 13 OF 21 · Choose the operation
13. Do not expect one individual setting to fix every region
Could we choose a lower opacity for each individual shape so that their full overlap matches a group fade? For n fully overlapping opaque shapes, set 1 − (1 − h)^n = g. Solving gives h = 1 − (1 − g)^(1/n), where h is the individual opacity.
With two identical black shapes and target group opacity g = 0.5, h = 1 − √0.5, about 0.292893. Two such shapes together have effective alpha 0.5 in their full overlap. The arithmetic works for that sample and the stated identical-colour example.
But a single-shape region now has alpha only about 0.292893 rather than 0.5. It no longer matches the group fade there. Regions with different overlap counts would require different corrections. With differently coloured shapes, matching combined alpha alone does not ensure matching the colour contributions either.
This is a practical reason to choose the appropriate operation instead of adjusting component sliders until one sample happens to look right. A local match can create a new mismatch elsewhere. Ask learners to test both the overlap and the edge of the design. The successful method preserves the intended relationship across the whole relevant image, rather than merely reproducing one sampled colour.
CHAPTER 14 OF 21 · Choose the operation
14. Treat pass-through and isolation as part of the setup
A group can be an organisational container, a compositing boundary or both, depending on the application and settings. An isolated group forms an intermediate image against transparency before interacting with the outside. A pass-through arrangement may let internal layers interact with the wider stack.
The W3C SVG rendering model distinguishes object and group opacity, while the Krita group-layer documentation explains its intermediate group result and pass-through option. These references establish why the group setup belongs in a reproducible test. They are not a claim that every editor uses identical defaults or interface labels.
When translating the lesson to software, create a small copy or new test document. Confirm normal compositing, group behaviour and the actual property being changed. Do not diagnose a complex existing file by repeatedly toggling settings without recording which change produced which result.
For a practical note, write “combined first, then faded” or “each component faded before combination” beside the saved comparison. Those descriptions are more durable than remembering a slider’s location in one interface version. They also make a handover clearer: another artist can understand the intended operation and test an equivalent setup in a different tool without assuming that a folder name guarantees the same result.
CHAPTER 15 OF 21 · Choose the operation
15. Keep masks and opacity at the intended level
A spatially varying group mask can act like a fade factor g(x, y) applied to the completed group at each point, within the specified compositing setup. Applying the same mask separately to every child is not generally equivalent in overlap regions. The earlier constant-opacity comparison becomes a local comparison wherever the mask has an intermediate value.
At a point where the mask value is 0.5, two fully overlapping opaque black child shapes illustrate the same 0.5 group alpha versus 0.75 individual combined alpha. At mask values zero and one, the difference vanishes under this model. The mismatch can therefore appear mainly along a soft transition.
This helps explain why a soft fade at the edge of a multi-part emblem may develop a darker overlap when the mask is repeated on each component. A group-level treatment can preserve the assembled silhouette while fading it against the page. Individual masks can deliberately reveal or alter internal relationships.
Actual applications offer multiple mask types and processing orders. Verify which operation the chosen mask performs; not every mask is a simple alpha multiplier. The controlled model gives a question to test, not an excuse to assume all masks behave alike. A small two-shape comparison can establish the relevant behaviour before the learner applies it to a detailed illustration.
CHAPTER 16 OF 21 · Choose the operation
16. Understand what flattening preserves and removes
Combining normal source-over layers into an intermediate image can preserve their current appearance when the correct colour and alpha are retained. It does not preserve all the editing choices that produced them. A flattened result may no longer allow the lower shape to be moved independently or its hidden area revised.
For the intended group fade, an editable group can provide the combined appearance without requiring destruction of the source layers. A separate flattened export can be useful for delivery, but it should not silently replace the only working file when future revisions matter.
Flattening against an opaque background is another distinct operation. The background becomes part of the image. Fading that flattened rectangle later also fades the baked-in background, which is not the same as fading only the emblem over a new external backdrop. Keep transparency and backdrop inclusion explicit.
The broader Digital Painting guide on purposeful layers and verifiable original work develops source-file and export decisions. This article adds a specific check: does the intermediate image contain just the intended group, or has it already incorporated a background? The distinction matters when an emblem moves from a white page to a coloured page or transparent delivery format.
CHAPTER 17 OF 21 · Check the finished work
17. Read soft edges as partial contributions
At a rasterised edge, a sample may have partial alpha rather than the full alpha of an interior point. The general two-component formula can describe a controlled local comparison with such supplied alpha values. Do not assume every edge sample behaves like the completely overlapping opaque interiors used in the first table.
Let a = 0.4 for the lower blue component, b = 0.6 for the upper red component and g = 0.5. The additional combined alpha in the individual treatment is g(1 − g)ab = 0.5 × 0.5 × 0.4 × 0.6 = 0.06. Over white, the final colour difference is 0.06(B − W) = (−0.06, −0.06, 0).
This is a local mathematical example, not a complete rasterisation model. Sampling, filtering and actual edge coverage can introduce other details. It shows why the discrepancy can vary across an edge rather than appear as one uniform strip.
For a visual check, inspect the design at its intended viewing size as well as at a useful magnification. A large zoom can expose sample behaviour, while the ordinary view reveals whether the change affects the reading of the image. Both questions matter. Avoid declaring the artwork successful or unsuccessful solely because a magnified pixel differs; connect the observation to the intended visual function.
Use two identical opaque black shapes on white, but change the requested group opacity to g = 0.4. A group fade gives alpha 0.4 and final linear-light coordinate (0.6, 0.6, 0.6). Fading each shape to 0.4 leaves background weight 0.6² = 0.36, giving (0.36, 0.36, 0.36) in their full overlap.
Add a third fully overlapping black shape at individual opacity 0.4. The surviving white contribution becomes 0.6³ = 0.216, so the effective alpha is 0.784. A single group fade of the completed opaque stack still has alpha 0.4.
| Changed exercise | Surviving white weight | Effective alpha |
|---|---|---|
| Completed opaque group faded once to 0.4 | 0.60 | 0.40 |
| Two opaque shapes each faded to 0.4 | 0.36 | 0.64 |
| Three opaque shapes each faded to 0.4 | 0.216 | 0.784 |
| Two shapes each at 1 − √0.6 | 0.60 in their overlap | 0.40 in their overlap only |
Before checking the table, ask the learner to predict which treatment preserves one flat faded silhouette. Then have them explain why the last row does not solve the whole-image problem in single-shape regions. A complete transfer answer uses the overlap count, the operation order and the intended appearance, rather than assuming that a slider label alone specifies the result.
CHAPTER 19 OF 21 · Check the finished work
19. Build a practical making and critique check
Begin with one clear visual intention and a two-shape test. Save the full-opacity reference, the group-faded version and the individually faded version with descriptive labels. Compare the overlap, the single-shape areas and the outside background. Change one factor at a time so the source of the difference remains visible.
For repair, use identical black shapes and focus on opacity. For stabilisation, use two different colours and reverse their order. For extension, introduce partial edge alpha, a soft mask or a new backdrop while keeping the model assumptions explicit. Fade prompts as the learner begins to predict the result independently.
A useful critique sentence connects observation to purpose: the overlap darkens because each translucent component is combined separately, which makes the emblem read as layered material rather than one faded silhouette. Another valid critique may prefer that layered reading. Both should point to evidence in the comparison.
When returning to a finished work, check the intended destination and reopen any exported file in an appropriate viewer. Record the application, relevant group setting, colour representation and backdrop used for the test. The outcome to look for is deliberate control: the learner can choose the operation that preserves or changes the intended relationship and can explain the choice without relying on trial and error alone.
CHAPTER 20 OF 21 · Check the finished work
20. Questions about fading groups and overlapping shapes
Is group opacity always the right choice?
No. It suits an intention to fade a completed internal appearance. Individual transparency can intentionally reveal overlaps or create a layered reading. The correct choice follows the visual purpose and the verified operation.
Why do the versions match where shapes do not overlap?
Only one component contributes at those points in the controlled model. The difference arises when individually faded components allow a lower contribution through an upper one. A matching non-overlap sample cannot prove whole-image equivalence.
Do two fifty-per-cent shapes make a fully opaque overlap?
Not under normal source-over in this example. They produce effective alpha 0.75, leaving 0.25 of the external background. Three produce 0.875. Alpha contributions combine through the remaining transparency rather than by simple addition.
Can one adjusted child opacity match a group everywhere?
Generally no. A value chosen to match one overlap count will differ in single-shape areas or regions with another count. Differently coloured components introduce colour contributions as well as combined alpha.
Does placing layers in a folder guarantee this group fade?
No. The application and group settings determine the operation. Check isolation, pass-through behaviour, compositing mode and which property is actually changed. Use a small controlled test and the relevant official documentation.
Does the model explain physical paint glazing?
It explains a defined digital compositing model. Physical pigments, scattering, absorption, surfaces and lighting require their own material account. A useful digital comparison should not be presented as a complete physical theory of transparent paint.
CHAPTER 21 OF 21 · Check the finished work
21. Continue through visual making, colour and source routes
Return to the Visual Arts subject guide for observation, composition, material decisions and critique. For editable making and delivery, use Digital Painting: deliberate pixels, editable layers and reliable exports and Digital Painting: purposeful layers, reliable colour and verifiable original work.
For colour representation and the basic alpha foundation, read colour spaces, gamma correction and digital displays. Its representation question is separate from, and relevant to, where opacity enters the compositing sequence. This article’s controlled examples keep that representation fixed.
The official references checked on 22 October 2026 are W3C Compositing and Blending Level 1, the SVG rendering model's object and group opacity account and Krita's group-layer manual. The sources explain the compositing framework and group behaviour; all emblem comparisons, calculations and transfer tasks here are original teaching examples.
Connect the making process with learning that transfers into life and explore the How X Works hub. A strong final explanation names the intended visual relationship, shows which operation produces it and checks the result where a difference could actually appear.