## 3. Case Study of Aesthetic Forms

### 3-1 Multiple-level Relative Motions

 Figure 3-1 Motions Illustration Rules: P0: P0(x,y) = (0, 0) P1: P1(angle) = P1(angle) + P1(angular increment)       P1(x) = P4(x) + P1(radius) * P1(cos(angle))         P1(y) = P4(y) + P1(radius) * P1(sin(angle)) P2: P2(angle) = P2(angle) + P2(angular increment)       P2(x) = P5(x) + P2(radius) * P2(cos(angle))         P2(y) = P5(y) + P2(radius) * P2(sin(angle)) P3: P3(angle) = P3(angle) + P3(angular increment)       P3(x) = P0(x) + P3(radius) * P3(cos(angle))         P3(y) = P0(y) + P3(radius) * P3(sin(angle)) P4: P4(x,y) = (P2(x,y) + P3(x,y)) / 2 P5: P5(x,y) = (P1(x,y) + P3(x,y)) / 2 P6: P6(x,y) = (P1(x,y) + P2(x,y) + P3(x,y)) / 3 Trajectory Recorded: P6

Table: Case 3-1.1 Parameters Assigned (Figure 3-1.1)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 180 0 0 Angular Increment 0.1300 -0.3900 0.1203 Radius(pixel) 150 110 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
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Figure 3-1.1 (12,000,000 iterations)

Table: Case 3-1.2 Parameters Assigned (Figure 3-1.2)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 0 0 Angular Increment 0.1300 -0.3900 0.1203 Radius(pixel) 150 150 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
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Figure 3-1.2 (12,000,000 iterations)

Table: Case 3-1.3 Parameters Assigned (Figure 3-1.3)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 0 0 Angular Increment -0.16003 0.48141 -0.04009 Radius(pixel) 150 150 60 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
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Figure 3-1.3 (12,000,000 iterations)

Table: Case 3-1.4 Parameters Assigned (Figure 3-1.4)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 0 0 Angular Increment -0.16003 0.48141 -0.00100 Radius(pixel) 150 150 60 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
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Figure 3-1.4 (12,000,000 iterations)

Table: Case 3-1.5 Parameters Assigned (Figure 3-1.5)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 0 180 Angular Increment 0.36003 -0.24000 0.16 Radius(pixel) 120 180 60 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
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Figure 3-1.5 (85,200 iterations)

Table: Case 3-1.6 Parameters Assigned (Figure 3-1.6)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 0 180 Angular Increment -1.2003 0.51 0.15 Radius(pixel) 120 180 60 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
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Figure 3-1.6 (270,000 iterations)

Table: Case 3-1.7 Parameters Assigned (Figure 3-1.7)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 90 0 Angular Increment 0.18 -0.24 -0.4207 Radius(pixel) 160 120 80 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
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Figure 3-1.7 (521,700 iterations)

Table: Case 3-1.8 Parameters Assigned (Figure 3-1.8)
 Point P1 P2 P3 Coordinate System P4 P5 P0 Initial Angle 0 90 0 Angular Increment 0.21 0.3509 -0.49 Radius(pixel) 200 40 90 Radius Increment None None None
* Positive angle means clockwise rotation, negative counterclockwise.
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Figure 3-1.8 (148,200 iterations)

CONTENTS:

 Index Introduction Methodology Case Study of Aesthetic Forms Conclusions