Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer Chapter 9 Chapter 9: Combining Transformation Operators

Chapter 9

Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer

Chapter 9: Combining Transformation Operators

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This Chapter: we will learn How and Costs of combine operators Inverse Operators Pivoted Scale/Rotate Programming Support

UWBGL

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Given vertex: Translate then Scale: If

Then

And

Translate Then Scale

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Example:

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Compact Representation

Computation Efficiency Cost to concatenate Worthwhile if uses operator many times

Concatenate:

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!Warning! Order of operation Recall …

So, if

Then, in general

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Example: Order of operation For: If and

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Reminder … Transforms Va

Translation (T) followed by Scale (S)

Vertex is to the left of the operators!!

In our case (row vectors): the following is undefined!!

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Inverse Transform: Undo

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For example:

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To undo (inverse):

If:

Then

Or:

Inverse of:

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Inverse of:

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Inverse of concatenated operator Apply the inverse in reverse order!

In general: Inverse is not unique E.g., R(θ), inverse can be

R(-θ) or R(-θ+360), or R(- θ+270) …

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Combining Translation and Scaling

Translate before scale to align vertex with origin “anchor” the vertex

E.g., scale rectangleby S(3,0.5) witha fixed anchor (Vc)

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Pivoted Scaling: Scaling with respect to

Pivot position:

E.g., scale rectanglewith respect topt=(1,5)

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Rotation with Arbitrary Pivot Pivot position:

E.g., rotate rectanglewith respect totop-right corner (pr)pt=(3,8)

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Tut 9.1: Simple Concatenation

Label B + C: Ma = S T Label D: loads Ma to MW All vertex goes through

V MW MV MP Rectangle transform by:

V Ma

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Tut 9.2: Order or concatenation

GUI Check box controls m_bTranslateFirst

Label B: Ma=ST or Ma=TS

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Matrix Stack: Push-down stack of matrices

Graphics API support for concatenation of transform operators (matrices)

Operations supported Push Pop Concatenation

Translate/scale/rotate Load/Store

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Tut 9.3: Working with Matrix Stack

Label C: Top of Stack <- ST Label D: Top of Stack <- TS Label E: MW<- Top of Stack

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Tut 9.4: Pivoted Scale/Rotate Implements:

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Tut 9.4: … details …

Label C computes:

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Tut 9.5: Transform Primitives

Label C1/C2: push/pop Label D: set up transform for

Drawing rectangle 1 Label F: set up transform for

Drawing rectangle 2

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Lib9: Drawing with MatrixStack

DrawHelper: Defines the Stack behavior

D3D_DrawHelper Defines D3D Matrix Stack

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Lib9: D3D_DrawHelper

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Lib9: XformInfo class Set/Get:

Scale/Translate/Rotate Pivot

SetupModelStack(): Calls DrawHelper’s

AccumulateModelTransform()

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Tut 9.6: Using XformInfo Identical to 9.5 … using XformInfo

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Tut 9.7: XformInfoControl CXformInfoControls class (MFC

Dialog) Replace onto main

TutorialDlg With a placeholder

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Using CXformInfoControl CModel must support

Label B: GetSelectedXform() SetSelectedXform()

CXformInfoControl Access model’s selected xform From theApp->GetModel().Get/Set selectedXform()

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Essentials of Interactive Computer Graphics: Concepts and Implementation K. Sung, P. Shirley, S. Baer Chapter 9 Chapter 9: Combining Transformation Operators