Transcript Essentials of Interactive Computer Graphics: Concepts and Implementation Chapter 9: Combining Transformation Operators Chapter 9 K.

Essentials of Interactive Computer Graphics: Concepts and Implementation
Chapter 9:
Combining
Transformation
Operators
Chapter 9
K. Sung, P. Shirley, S. Baer
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
This Chapter: we will learn
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How and Costs of combine operators
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Inverse Operators
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Pivoted Scale/Rotate
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Programming Support
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UWBGL
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
Translate Then Scale
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Given vertex:
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Translate then Scale:
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If
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Then
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And
Chapter 9
K. Sung, P. Shirley, S. Baer
Essentials of Interactive Computer Graphics: Concepts and Implementation
Example:
Chapter 9
K. Sung, P. Shirley, S. Baer
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Concatenate:
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Compact Representation
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Computation Efficiency
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Cost to concatenate
Worthwhile if uses operator many times
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
!Warning! Order of operation
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Recall …
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So, if
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Then, in general
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Example: Order of operation
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For:
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If
and
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Reminder …
Transforms Va
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Translation (T) followed by
Scale (S)
Vertex is to the left of the operators!!
In our case (row vectors): the following
is undefined!!
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
Inverse Transform: Undo
Chapter 9
K. Sung, P. Shirley, S. Baer
Essentials of Interactive Computer Graphics: Concepts and Implementation
For example:
Chapter 9
K. Sung, P. Shirley, S. Baer
Essentials of Interactive Computer Graphics: Concepts and Implementation
Inverse of:
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To undo (inverse):
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If:
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Then
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Or:
Chapter 9
K. Sung, P. Shirley, S. Baer
Essentials of Interactive Computer Graphics: Concepts and Implementation
Inverse of:
Chapter 9
K. Sung, P. Shirley, S. Baer
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Inverse of concatenated operator
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Apply the inverse in reverse order!
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In general: Inverse is not unique
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E.g., R(θ), inverse can be
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R(-θ) or
R(-θ+360), or R(- θ+270) …
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Combining Translation and Scaling
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Translate before scale to
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align vertex with origin
“anchor” the vertex
E.g., scale rectangle
by S(3,0.5) with
a fixed anchor (Vc)
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
Pivoted Scaling:
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Scaling with respect to
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Pivot position:
E.g., scale rectangle
with respect to
pt=(1,5)
Chapter 9
K. Sung, P. Shirley, S. Baer
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Rotation with Arbitrary Pivot
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Pivot position:
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E.g., rotate rectangle
with respect to
top-right corner (pr)
pt=(3,8)
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Tut 9.1: Simple Concatenation
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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
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Tut 9.2: Order or concatenation
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GUI Check box controls
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m_bTranslateFirst
Label B:
 Ma=ST or
 Ma=TS
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Matrix Stack:
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Push-down stack of matrices
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Graphics API support for concatenation of
transform operators (matrices)
Operations supported
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Push
Pop
Concatenation
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Translate/scale/rotate
Load/Store
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Tut 9.3: Working with Matrix Stack
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Label C: Top of Stack <- ST
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Label D: Top of Stack <- TS
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Label E: MW<- Top of Stack
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Tut 9.4: Pivoted Scale/Rotate
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Implements:
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
Tut 9.4: … details …
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Label C computes:
Chapter 9
K. Sung, P. Shirley, S. Baer
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Tut 9.5: Transform Primitives
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Label C1/C2: push/pop
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Label D: set up transform for
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Drawing rectangle 1
Label F: set up transform for
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Drawing rectangle 2
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Lib9: Drawing with MatrixStack
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DrawHelper:
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Defines the Stack behavior
D3D_DrawHelper
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Defines D3D Matrix Stack
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
Lib9: D3D_DrawHelper
Chapter 9
K. Sung, P. Shirley, S. Baer
Essentials of Interactive Computer Graphics: Concepts and Implementation
Lib9: XformInfo class
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Set/Get:
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Scale/Translate/Rotate
Pivot
SetupModelStack():
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Calls DrawHelper’s
AccumulateModelTransform()
Chapter 9
K. Sung, P. Shirley, S. Baer
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Tut 9.6: Using XformInfo
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Identical to 9.5 … using XformInfo
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Tut 9.7: XformInfoControl
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CXformInfoControls class (MFC Dialog)
Replace onto main
TutorialDlg
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With a placeholder
Chapter 9
Essentials of Interactive Computer Graphics: Concepts and Implementation
K. Sung, P. Shirley, S. Baer
Using CXformInfoControl
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CModel must support
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Label B:
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GetSelectedXform()
SetSelectedXform()
CXformInfoControl
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Access model’s selected xform
From theApp->GetModel().Get/Set
selectedXform()
Chapter 9