Transforming one triangle onto another congruent triangle in 2-D

1
Transforming one triangle onto another congruent
triangle in 2-D
Transformation
Two congruent triangles
1) Translate A to A 2) Rotate
2
Find the Bisecting Lines

• Find the line bisecting (perpendicular to the
  line connecting)
• each pair of points.

3
Find the Rotation Axis
2) Their intersection is the rotation axis,
called the Chasles center.
Notice Both metrics look the same from O
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Transform Two 3-D Metrics into Coincidence
Arbitrary orientations of asymmetric
tetrahedra Viewed along an axis that gives
identical projections, rotated w.r.t. one another.
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One method Translate, then Rotate
1) Translate
2) Rotate
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Find the Planes Bisecting the Projected Points
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Unique Alternative Screw Rotation
Chasles Center
Translation is along axis of rotation
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Simple Reflection
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Reflection Across Shifted Plane (I)

1. translate
2. reflect
3. translate

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Reflection Across Shifted Plane (II)

1. reflect
2. translate

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Double Reflection
Sequential reflection across two plane at an
angle ? is equivalent to a rotation about their
intersection by 2?.
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Translation by Two Reflections
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Triple Rotation About Triangle Vertices
Sequential rotations by 2?, 2?, 2? about A, B, C
(in any order) is the identity transformation.