[Drawkit] Transforms / ScaleBy

[Allan Daly]

Very useful info (as always). Thank you. -Allan


On Apr 30, 2009, at 8:16 PM, Graham Cox wrote:

>
> On 01/05/2009, at 12:45 PM, Allan Daly wrote:
>
>> Mike, Graham,
>>
>> Picking up on this thread ... for my DXF importer I need to be able  
>> to scale DKShapeGroups by a scale factor that I read out of the DXF  
>> INSERT entity data. Actually there can be separate X and Y scale  
>> factors. How do I apply these to DKShapeGroups, or for that matter  
>> any DKDrawableObject?
>
> To a large extent, DK is designed to shield you from dealing with  
> NSAffineTransform objects directly in most cases. If you are working  
> with the built-in objects, there are very few places where the  
> transforms are exposed. It's only when you get into low-level  
> subclassing that they become necessary to deal with.
>
> A drawable's -setLocation:, -setSize: and -setAngle: methods  
> internally set up transforms for translation, scaling and rotation  
> respectively.
>
> To scale an object, pass the desired size to -setSize: and it will  
> transform itself as necessary. This works with groups as well.
>
> If you want to scale an object by a certain factor (x2, say) then  
> you need to do a small calculation by taking the current size,  
> multiplying it by the factors then setting the resulting size.  
> There's no constraint on the scale factors being equal in X and Y.
>
> The other thing DK shields you from is the transform origin. When  
> dealing with transforms directly, you always have to allow for the  
> origin of the coordinate system, which is where everything is  
> measured from. For our purposes it's more useful to allow each  
> object to effectively define its own local origin, so that sizing  
> and rotation operations are performed relative to this point. By  
> default DK's shape objects set this at their centre, so doubling a  
> shape's size expands it about that centre point. Using -setOffset:  
> allows you to move that point elsewhere relative to the shape's  
> bounds, so if you wanted the top, left corner to remain where it is  
> when doubling the size you could set the offset to {-0.5,-0.5}  
> before calling -setSize: (The offset is always expressed as if the  
> bounds were a 1 x 1 square).
>
> The only slightly tricky possibility when using -setSize: is that if  
> the object is already rotated, -setSize: operates as if the rotation  
> weren't there - in other words the edge lengths of the rotated shape  
> are always correctly set to the size you pass, and the unseen bounds  
> will vary as needed. Mostly that's exactly what you want and is  
> entirely intuitive, but if for example the DXF scale factors are  
> expressed in terms of the scaled edges of the bounds rect, even with  
> any rotation applied, you'll end up having to use a bit of  
> trigonometry to work out how the bounds sizes are affected. If that  
> turns out to be the case (probably unlikely) I can help you work out  
> what to do.
>
>> From reading through the message string below I can see that  
>> NSAffineTransformation objects are involved, and from looking at  
>> the API documentation on that I sort of get it, but frankly it  
>> eludes me right now. Could either of you provide any help to get me  
>> pointed in the right direction on this? And/or do you know any good  
>> links to send me that would help me understand what the heck an  
>> AffineTransformation is and how I should use it? Seem to me that I  
>> fundamentally do not understand these Transformation objects and I  
>> would like to.
>>
>
> A good starting point is probably the wikipedia article: http://en.wikipedia.org/wiki/Affine_transformation 
>  though it suffers from the usual problem of wikipedia articles in  
> that it dives into the maths without enough conceptual stuff.
>
> A somewhat more Cocoa-oriented approach is here: http://cocoadevcentral.com/articles/000045.php
>
> This is an excellent step-by-step guide, and was where I first got  
> started with NSAffineTransform.
>
> Hope that helps,
>
> --Graham
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