Synchronize transform matrix of superview and individual views in different coordinate space

Question

Given following view hierarchy:

root (e.g. view of a view controller)
  |_superview: A view where we will draw a cross using core graphics
    |_container: Clips subview
      |_subview: A view where we will show a cross adding subviews, which has to align perfectly with the cross drawn in superview
        |_horizontal line of cross
        |_vertical line of cross

Task:

The crosses of superview and subview have to be always aligned, given a global transform. More details in "requirements" section.

Context:

The view hierarchy above belongs to a chart. In order to provide maximal flexibility, it allows to present chart points & related content in 3 different ways:

1. Drawing in the chart's base view (superview) draw method.

2. Adding subviews to subview. subview is transformed on zoom/pan and with this automatically its subviews.

3. Adding subviews to a sibling of subview. Not presented in view hierarchy for simplicity and because it's not related with the problem. Only mentioning it here to give an overview. The difference between this method and 2., is that here the view is not transformed, so it's left to the implementation of the content to update "manually" the transform of all the children.

Maximal flexibility! But with this comes the cost that it's a bit tricky to implement. Specifically point 2.

Currently I got zoom/pan working by basically processing the transforms for superview core graphics drawing and subview separately, but this leads to redundancy and error-proneness, e.g. repeated code for boundary checks, etc.

So now I'm trying to refactor it to use one global matrix to store all the transforms and derive everything from it. Applying the global matrix to the coordinates used by superview to draw is trivial, but deriving the matrix of subview, given requirements listed in next section, not so much.

I mention "crosses" in the view hierarchy section because this is what I'm using in my playgrounds as a simplified representation of one chart point (with x/y guidelines) (you can scroll down for images and gists).

Requirements:

1. The content can be zoomed and panned.
2. The crosses stay always perfectly aligned.
3. subview's subviews, i.e. the cross line views can't be touched (e.g. to apply transforms to them) - all that can be modified is subview's transform.
4. The zooming and panning transforms are stored only in a global matrix matrix.
5. matrix is then used to calculate the coordinates of the cross drawn in superview (trivial), as well as the transform matrix of subview (not trivial - reason of this question).
   • Since it doesn't seem to be possible to derive the matrix of subview uniquely from the global matrix, it's allowed to store additional data in variables, which are then used together with the global matrix to calculate subview's matrix.
6. The size/origin of container can change during zoom/pan. The reason of this is that the labels of the y-axis can have different lengths, and the chart is required to adapt the content size dynamically to the space occupied by the labels (during zooming and panning).
7. Of course when the size of container changes, the ratio of domain - screen coordinates has to change accordingly, such that the complete original visible domain continues to be contained in container. E.g if I'm displaying an x-axis with a domain [0, 10] in a container frame with a width of 500pt, i.e. the ratio to convert a domain point to screen coordinates is 500/10=50, and shrink the container width to 250, now my [0, 10] domain, which has to fit in this new width, has a ratio of 25.
8. It has to work also for multiple crosses (at the same time) and arbitrary domain locations for each. This should happen automatically by solving 1-7 but mentioning it for completeness.

What I have done:

Here are step-by-step playgrounds I did to try to understand the problem better:

Step 1 (works):

Build hierarchy as described at the beginning, displaying nothing but crosses that have to stay aligned during (programmatic) zoom & pan. Meets requirements 1, 2, 3, 4 and 5:

Gist with playground.

Particularities here:

• I skipped container view, to keep it simple. subview is a direct subview of superview.
• subview has the same size as superview (before zooming of course), also to keep it simple.
• I set the anchor point of subview to the origin (0, 0), which seems to be necessary to be in sync with the global matrix.
• The translation used for the anchor change has to be remembered, in order to apply it again together with the global matrix. Otherwise it gets overwritten. For this I use the variable subviewAnchorTranslation. This belongs to the additional data I had in mind in the bullet under requirement 5.

Ok, as you see everything works here. Time to try the next step.

Step 2 (works):

A copy of step 1 playground with modifications:

• Added container view, resembling now the view hierarchy described at the beginning.
• In order for subview, which is now a subview of container to continue being displayed at the same position, it has to be moved to top and left by -container.origin.
• Now the zoom and pan calls are interleaved randomly with calls to change the frame position/size of container.

The crosses continue to be in sync. Requirements met: All from step 1 + requirement 6. Gist with playground

Step 3 (doesn't work):

So far I have been working with a screen range that starts at 0 (left side of the visible playground result). Which means that container is not fulfilling it's function to contain the range, i.e. requirement 7. In order to meet this, container's origin has to be included in the ratio calculation.

Now also subview has to be scaled in order to fit in container / display the cross at the correct place. Which adds a second variable (first being subviewAnchorTranslation), which I called contentScalingFactor, containing this scaling, that has to be included in subview's matrix calculation.

Here I've done multiple experiments, all of them failed. In the current state, subview starts with the same frame as container and its frame is adjusted + scaled when the frame of container changes. Also, subview being now inside container, i.e. its origin being now container's origin and not superview's origin, I have to set update its anchor such that the origin is not at (0,0) but (-x,-y), being x and y the coordinates of container's origin, such that subview continues being located in relation to superview's origin. And it seems logical to update this anchor each time that container changes its origin, as this changes the relative position from content's origin to superview's origin.

I uploaded code for this - in this case a full iOS project instead of only a playground (I thought initially that it was working and wanted to test using actual gestures). In the actual project I'm working on the transform works better, but I couldn't find the difference. Anyway it doesn't work well, at some point there are always small offsets and the points/crosses get out of sync.

Github project

Ok, how do I solve this such that all the conditions are met. The crosses have to stay in sync, with continuous zoom/pan and changing the frame of container in between.

Answer 1

The present answer allows for any view in the Child hierarchy to be arbitrarily transformed. It does not track the transformation, merely converts a transformed point, thus answers the question:

What are the coordinates of a point located in a subview in the coordinate system of another view, no matter how much that subview has been transformed.

To decouple the Parent from the clipping Container and offer a generic answer, I propose place them at the same level conceptually, and in different order visually ^(†):

Use a common superview

To apply the scrolling, zooming or any other transformation from the Child to the Parent, go through common superview (named Coordinator in the present example).

The approach is very similar to this Stack Overflow answer where two UIScrollView scroll at different speed.

Notice how the red hairline and black hairline overlap, regardless of the position, scrolling, transform of any and all off the views in the Child hierarchy, including that of Container.

↻ replay animation

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Code

Coordinate conversion

Simplified for clarity, using an arbitrary point (50,50) in the coordinate system of the Child view (where that point is effectively drawn), and convert it in the Parent view system looks like this:

func coordinate() {
    let transfer = theChild.convert(CGPoint(x:50, y:50), to: coordinator)
    let final = coordinator.convert(transfer, to: theParent)
    theParent.transformed = final
    theParent.setNeedsDisplay()
}

Zoom & Translate Container

func zoom(center: CGPoint, delta: CGPoint) {
    theContainer.transform = theContainer.transform.scaledBy(x: delta.x, y: delta.y)
    coordinate()
}

func translate(delta: CGPoint) {
    theContainer.transform = theContainer.transform.translatedBy(x: delta.x, y: delta.y)
    coordinate()
}

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(†) I have renamed Superview and Subview to Parent and Child respectively.