drawingml subject: transforms

Shape Transforms

DrawingML

Where are we?

spTree

nvGrpSpPr grpSpPr sp

nvSpPr spPr

style txBody

xfrm geo

fillProperties lineProperties

effectProperties scene3D

sp3D bwMode

Transform “Variables”

• Shapes– Offset X– Offset Y– Extents X– Extents Y

• Group Shapes– Offset X– Offset Y– Extents X– Extents Y– Child Offset X– Child Offset Y– Child Extents X– Child Extents Y

Coordinate Space( 0,0 )

X-Axis

Y-A

xis

2D Units measures in EMUs ( 914400 EMUs per inch )

Shape Transform “Variables”

Extent X

Offset XExtent Y

Offset Y

( 0,0 )

Group Transform “Variables”

( 0,0 )

Offset X == Ch Offset X

Offset Y == Ch Offset Y

Extent Y == Ch Extent Y

Extent X == Ch Extent X

Lesson #1

• When a group is created the group’s offset and extents are equal to the children’s offset and extents.

Offset_X == ChOffset_X

Offset_Y == ChOffset_Y

Extent_X == Extent_X

Extent_Y == Extent_Y

Lesson #2

• Effect Bounds do not relate to extent variables for shapes or groups

( 0,0 )

Offset X == Ch Offset X

Offset Y == Ch Offset Y

Extent Y == Ch Extent Y

Extent X == Ch Extent X

Case 1Scenario: A slide contains two shapes, a block arrow and a triangle.

X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset

Extent

Offset

Extent

Child Shapes

Bef

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Aft

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Case 2Scenario: Given Case 1, move the block arrow to the right

X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 2673 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

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Case 3Scenario: Given Case 1, resize block arrow to 150% ( towards the BR of the slide )

X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 914 1524

Extent 1467 726

Offset 3657 3449

Extent 1060 914

Child Shapes

X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

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Case 4Scenario: Given Case 1, rotate the block arrow 90 degrees, clockwise

X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

er

Rotation = 5,400,000

Lesson #3

• Rotation does not change the offset or extents of the target shape– But it might change the offset or extents of a

containing shape– “Resolved” at rendering time

Case 5Scenario: Given Case 1, group both shapes

X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

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The Details

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Explanation

First determine the offset for the group:

Offset_X = Min ( Offset_X, Offset_X )= Min ( 914, 3657 )= 914

Offset_Y = Min ( Offset_Y, Offset_Y )= Min ( 1524, 3449 )= 1524

Next determine the extent of the group:

Extent_X = Max ( ( Offset_X + Extent_X - Offset_X ) ,( Offset_X + Extent_X - Offset_X ) )

= Max ( 978, 3803 ) = 3803

Extent_Y = Max ( ( Offset_Y + Extent_Y - Offset_Y ) , ( Offset_Y + Extent_Y - Offset_Y ) )

= Max ( 484, 2839 )= 2839

And based on Lesson #1, the children values are the same …

X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

Descrepancies between the table and details are due to rounding errors

Case 6Scenario: Given Case 5, move the group to the right

X Y

Offset 4197 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

er

The Details

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Explanation

Because the entire group was moved to the right ( along the X-axis ) the Offset_X value of the group was the only variable that changed.

X Y

Offset 4197 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape


Case 7Scenario: Given Case 5, resize the group to 50% ( towards the TL of the slide )

X Y

Offset 914 1524

Extent 1919 1413

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

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The Details

Explanation

Because we have scaled the group down by approximately 50% and we have not moved it, we are only modifying the group shape extents. The modification, not surprisingly, is ( approximately ) 50%.

Extent_X = Extent_X * .50= 3803 * .5= 1901

Extent_Y = Extent_Y * .50= 2840 * .5= 1420

X Y

Offset 914 1524

Extent 1919 1413

ChOffset 914 1524

ChExtent 3803 2840

Group Shape ( new )


X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape ( old )

Case 8Scenario: Given Case 5, rotate the group shape 90 degrees, clockwise

X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

er


Case 9Scenario: Given Case 5, rotate the block arrow 90 degrees, clockwise

X Y

Offset 1161 1277

Extent 3557 3087

ChOffset 1161 1277

ChExtent 3557 3087

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

er


The Details

Explanation

Since the block arrow ( a child shape ) was rotated, first a rotation value is applied to that spPr.

As a result of the application of rotation on the block arrow, the bounding box of the block arrow changes; this change ripples into the dimension of the group.

Leaving the calculation of the new bounding for the block arrow as an exercise for the reader, a quick survey illustrates the general change. Observe:

X Y

Offset 1161 1277

Extent 3557 3087

ChOffset 1161 1277

ChExtent 3557 3087

Group Shape ( new )


X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape ( old )

• The block arrow’s bounding box ( looking at the resultant picture ) is farther along the X-axis. Note the group shape’s X-offset is 247 units longer.

• Because the X-Offset is longer, and the triangle has not moved, the group shape’s X-extent is shorter … by 247 units.

• Since rotation occurs against the center of the selection, the top of the block arrow’s bounding box is a shorter distance from the Y-axis. Note the group shape’s Y-offset is 247 units shorter.

• Because the Y-Offset is shorter, and the triangle has not moved, the group shape’s Y-extent is longer … by 247 units.

This is much easier to follow with matrix math, but I didn’t want to force this on folks …

Lesson #4

• Rotation is done relative to the center of the selection

Case 10Scenario: Given Case 5, move the triangle to the right

X Y

Offset 914 1524

Extent 5618 2840

ChOffset 914 1524

ChExtent 5618 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 5472 3449

Extent 1060 914

Child Shapes

X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

er

The Details

X Y

Offset 914 1524

Extent 978 484

Offset 5472 3449

Extent 1060 914

Child Shapes

Explanation

Since we moved just the triangle shape along the X-axis, the triangle’s spPr gets an updated Offset_X. Then we must recompute the group shape transform:

First determine the offset for the group:

Offset_X = Min ( Offset_X, Offset_X )= Min ( 914, 5472 )= 914

Offset_Y = Min ( Offset_Y, Offset_Y )= Min ( 1524, 3449 )= 1524

Next determine the extent of the group:

Extent_X = Max ( ( Offset_X + Extent_X - Offset_X ) ,( Offset_X + Extent_X - Offset_X ) )

= Max ( 5472 , 5618 ) = 5618

Extent_Y = Max ( ( Offset_Y + Extent_Y - Offset_Y ) , ( Offset_Y + Extent_Y - Offset_Y ) )

= Max ( 484, 2839 )= 2839

And based on Lesson #1, the children values are the same …

X Y

Offset 914 1524

Extent 5618 2840

ChOffset 914 1524

ChExtent 5618 2840

Group Shape


Case 11Scenario: Given Case 5, ungroup

X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

er


X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 4197 1524

Extent 978 484

Offset 6941 3449

Extent 1060 914

Child Shapes

X Y

Offset 4197 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

er

The Details

X Y

Offset 4197 1524

Extent 3803 2840

Offset 914 1524

Extent 3803 2840

Child Shapes ( Old )

Explanation

Since the group was moved along the X-axis, we need to determine new X-axis values for the child shapes. The child shapes still have their original offset and extent values.

Offset_X = G Offset_X – G chOffset_X + Offset_X= 4197 – 914 + 914= 4197

Offset_Y = G Offset_Y – G chOffset_Y + Offset_Y= 1524 – 1524 + 1524= 1524

Offset_X = G Offset_X – G chOffset_X + Offset_X= 4197 – 914 + 3657= 6940

Offset_Y = G Offset_Y – G chOffset_Y + Offset_Y= 1524 – 1524 + 3449= 3449

X Y

Offset 4197 1524

Extent 978 484

Offset 6941 3449

Extent 1060 914

Child Shape ( New)

Discrepancies between the table and details are due to rounding errors


X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 914 1524

Extent 493 241

Offset 2298 2482

Extent 535 454

Child Shapes

X Y

Offset 914 1524

Extent 1919 1413

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

er

The Details

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes ( Old )

Explanation

Since the group shape was scaled down by 50% but not moved, only the block arrow’s offset values will be unchanged.

To determine the two shape’s extents, we simply apply the scaling factor:

Extent_X = Extent_X * .5 Extent_Y = Extent_Y * .5= 978 * .5 = 484 * .5= 489 = 242

Extent_X = Extent_X *.5 Extent_Y = Extent_Y *.5= 1060 * .5 = 914 * .5

= 535 = 457

X Y

Offset 914 1524

Extent 493 241

Offset 2298 2482

Extent 535 454

Child Shape ( New)

Discrepancies between the table and details are due to rounding errors

To determine the offsets, we need to scale the values by the ratio of the group shape’s extent values. We first translate to zero, apply the scale, and then translate back.

Offset_X = ( Offset_X – G chOff_X ) * ( G extent_X / G chEnt_X ) + G Offset_X= ( 914 – 914 ) * ( 1919 / 3803 ) + 914= 914

Offset_Y = ( Offset_Y – G chOff_Y ) * ( G extent_Y / G chEnt_Y ) + G Offset_Y= ( 1524 – 1524 ) ( 1413 / 2840 ) + 1524= 1524

Offset_X = ( Offset_X – G chOff_X ) * ( G extent_X / G chEnt_X ) + G Offset_X= ( 3657 – 914 ) * ( 1919 / 3803 ) + 914= 2285

Offset_Y = ( Offset_Y – G chOff_Y ) * ( G extent_Y / G chEnt_Y ) + G Offset_Y= ( 3449 – 1524 ) ( 1413 / 2840 ) + 1524= 2487

Lesson #5

• Scaling is always done using the ratio of the group extents to the group children extents ( even for calculating offsets )


X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 3504 1289

Extent 978 484

Offset 1323 3858

Extent 1060 914

Child Shapes

X Y

Offset 914 1524

Extent 3803 2840

ChOffset 914 1524

ChExtent 3803 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

er



X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

X Y

Offset 1161 1277

Extent 3557 3087

ChOffset 1161 1277

ChExtent 3557 3087

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 3657 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

er




X Y

Offset

Extent

ChOffset

ChExtent

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 5472 3449

Extent 1060 914

Child Shapes

X Y

Offset 914 1524

Extent 5618 2840

ChOffset 914 1524

ChExtent 5618 2840

Group Shape

X Y

Offset 914 1524

Extent 978 484

Offset 5472 3449

Extent 1060 914

Child Shapes

Bef

ore

Aft

er

Disclaimer

This presentation is for informational purposes only, and should not be relied upon as a substitute or replacement for Microsoft formal file format documentation, which is available at the following website: https://msdn.microsoft.com/en-us/library/cc313118(v=office.12).aspx. Any views or opinions presented in this material are solely those of the author and do not necessarily represent those of Microsoft. Microsoft disclaims all liability for mistakes or inaccuracies in this presentation.

https://msdn.microsoft.com/en-us/library/cc313118(v=office.12).aspx

https://msdn.microsoft.com/en-us/library/cc313118(v=office.12).aspx

drawingml subject: transforms

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