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3. Case Study of Aesthetic Forms

3-4 Pursuit Multiple-level Relative Motions

3-4-1 Case I: Pursue the farthest coordinate system


Figure 3-4a Motions Illustration

Initial State:
P4 pursues P1, velocity = 1 (pixels per iteration)

Rules:
P0: P0(x, y) = (0, 0)

P1: P1(angle) = P1(angle) + P1(angular increment)

     P1(x) = P3(x) + P1(radius) * P1(cos(angle))

     P1(y) = P3(y) + P1(radius) * P1(sin(angle))

P2: P2(angle) = P2(angle) + P2(angular increment)

     P2(x) = P3(x) + P2(radius) * P2(cos(angle))

     P2(y) = P3(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))

We set the rules of P4 as follow below:

P4: d1 = distance(P1, P4)
     d2 = distance(P2, P4)
     d3 = distance(P3, P4)
     if d1 equals the greatest of d1, d2 and d3, then
          let P4 pursue P1
     end if
     if d2 equals the greatest of d1, d2 and d3, then
          let P4 pursue P2
     end if
     if d3 equals the greatest of d1, d2 and d3, then
          let P4 pursue P3
     end if
Trajectory Recorded: P4

Table: Case 3-4.1 Parameters Assigned (Figure 3-4.1)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
0
180
0
Angular Increment
0.05
-0.15
0.06404658
Radius(pixel)
300
220
80
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.1 (18,000,000 iterations)
Table: Case 3-4.2 Parameters Assigned (Figure 3-4.2)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
0
180
0
Angular Increment
0.05
-0.15
0.06405
Radius(pixel)
300
120
80
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.2 (18,000,000 iterations)
Table: Case 3-4.3 Parameters Assigned (Figure 3-4.3)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
0
180
0
Angular Increment
0.03
-0.27
0.06405
Radius(pixel)
300
120
80
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.3 (18,000,000 iterations)
Table: Case 3-4.4 Parameters Assigned (Figure 3-4.4)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
0
180
0
Angular Increment
0.03
-0.27
0.06405
Radius(pixel)
300
220
80
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.4 (18,000,000 iterations)
Table: Case 3-4.5 Parameters Assigned (Figure 3-4.5)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
180
0
0
Angular Increment
-0.03
0.27
0.06405
Radius(pixel)
300
150
80
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.5 (18,000,000 iterations)
Table: Case 3-4.6 Parameters Assigned (Figure 3-4.6)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
0
180
0
Angular Increment
0.05
-0.15
0.154047
Radius(pixel)
300
120
80
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.6 (18,000,000 iterations)
Table: Case 3-4.7 Parameters Assigned (Figure 3-4.7)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
0
180
0
Angular Increment
0.07
-0.14
0.284047
Radius(pixel)
300
120
80
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.7 (18,000,000 iterations)

 

3-4-2 Case I: Pursue the nearest coordinate system

We modify the rules of P4 as follow below:

P4: d1 = distance(P1, P4)
     d2 = distance(P2, P4)
     d3 = distance(P3, P4)
     if d1 equals the smallest of d1, d2 and d3, then
          let P4 pursue P1
     end if
     if d2 equals the smallest of d1, d2 and d3, then
          let P4 pursue P2
     end if
     if d3 equals the smallest of d1, d2 and d3, then
          let P4 pursue P3
     end if
Trajectory Recorded: P4

Table: Case 3-4.8 Parameters Assigned (Figure 3-4.8)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
0
0
0
Angular Increment
-0.47000000
0.51000000
0.48404658
Radius(pixel)
170
120
200
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.8 (18,000,000 iterations)
Table: Case 3-4.9 Parameters Assigned (Figure 3-4.9)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
0
180
0
Angular Increment
0.420100
-0.640300
0.384047
Radius(pixel)
200
130
200
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.9 (12,000,000 iterations)
Table: Case 3-4.10 Parameters Assigned (Figure 3-4.10)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
180
0
0
Angular Increment
0.140000
-0.260010
0.284047
Radius(pixel)
100
150
180
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.10 (18,000,000 iterations)
Table: Case 3-4.11 Parameters Assigned (Figure 3-4.11)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
0
180
0
Angular Increment
0.240000
-0.080000
0.284047
Radius(pixel)
300
120
80
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.11 (18,000,000 iterations)
Table: Case 3-4.12 Parameters Assigned (Figure 3-4.12)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
0
180
0
Angular Increment
-0.180000
-0.030010
0.684047
Radius(pixel)
300
120
80
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.12 (18,000,000 iterations)
Table: Case 3-4.13 Parameters Assigned (Figure 3-4.13)
Point
P1
P2
P3
Coordinate System
P3
P3
P0
Initial Angle
180
0
0
Angular Increment
0.160000
-0.250010
0.684047
Radius(pixel)
300
220
80
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.13 (18,000,000 iterations)

 

3-4-3 Case II: Pursue the farthest coordinate system


Figure 3-4b Motions Illustration

Initial State:
P4 pursues P1, velocity = 1 (pixels per iteration)

Rules:
P0: P0(x, y) = (0, 0)

P1: P1(angle) = P1(angle) + P1(angular increment)

     P1(x) = P2(x) + P1(radius) * P1(cos(angle))

     P1(y) = P2(y) + P1(radius) * P1(sin(angle))

P2: P2(angle) = P2(angle) + P2(angular increment)

     P2(x) = P3(x) + P2(radius) * P2(cos(angle))

     P2(y) = P3(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))

We set the rules of P4 as follow below:

P4: d1 = distance(P1, P4)
     d2 = distance(P2, P4)
     d3 = distance(P3, P4)
     if d1 equals the greatest of d1, d2 and d3, then
          let P4 pursue P1
     end if
     if d2 equals the greatest of d1, d2 and d3, then
          let P4 pursue P2
     end if
     if d3 equals the greatest of d1, d2 and d3, then
          let P4 pursue P3
     end if
Trajectory Recorded: P4

Table: Case 3-4.14 Parameters Assigned (Figure 3-4.14)
Point
P1
P2
P3
Coordinate System
P2
P3
P0
Initial Angle
0
0
0
Angular Increment
0.035330
-0.547783
-0.047300
Radius(pixel)
150
100
150
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.14 (12,000,000 iterations)
Table: Case 3-4.15 Parameters Assigned (Figure 3-4.15)
Point
P1
P2
P3
Coordinate System
P2
P3
P0
Initial Angle
0
0
0
Angular Increment
-0.047300
-0.547783
0.035330
Radius(pixel)
150
100
150
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.15 (12,000,000 iterations)
Table: Case 3-4.16 Parameters Assigned (Figure 3-4.16)
Point
P1
P2
P3
Coordinate System
P2
P3
P0
Initial Angle
0
0
0
Angular Increment
0.047300
-0.035330
0.547783
Radius(pixel)
150
150
100
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.16 (12,000,000 iterations)

 

3-4-4 Case II: Pursue the nearest coordinate system

We modify the rules of P4 as follow below:

P4: d1 = distance(P1, P4)
     d2 = distance(P2, P4)
     d3 = distance(P3, P4)
     if d1 equals the smallest of d1, d2 and d3, then
          let P4 pursue P1
     end if
     if d2 equals the smallest of d1, d2 and d3, then
          let P4 pursue P2
     end if
     if d3 equals the smallest of d1, d2 and d3, then
          let P4 pursue P3
     end if
Trajectory Recorded: P4

Table: Case 3-4.17 Parameters Assigned (Figure 3-4.17)
Point
P1
P2
P3
Coordinate System
P2
P3
P0
Initial Angle
0
0
0
Angular Increment
-0.5967700
0.3090170
-0.4075677
Radius(pixel)
70
100
180
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.17 (12,000,000 iterations)
Table: Case 3-4.18 Parameters Assigned (Figure 3-4.18)
Point
P1
P2
P3
Coordinate System
P2
P3
P0
Initial Angle
0
0
0
Angular Increment
0.5967700
0.3090170
0.4075677
Radius(pixel)
70
100
180
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.18 (12,000,000 iterations)
Table: Case 3-4.19 Parameters Assigned (Figure 3-4.19)
Point
P1
P2
P3
Coordinate System
P2
P3
P0
Initial Angle
0
0
0
Angular Increment
0.8967700
-0.3090170
0.5075677
Radius(pixel)
70
100
180
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.19 (12,000,000 iterations)
Table: Case 3-4.20 Parameters Assigned (Figure 3-4.20)
Point
P1
P2
P3
Coordinate System
P2
P3
P0
Initial Angle
0
0
0
Angular Increment
0.6967700
-0.3090170
0.5075677
Radius(pixel)
170
100
180
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.20 (12,000,000 iterations)
Table: Case 3-4.21 Parameters Assigned (Figure 3-4.21)
Point
P1
P2
P3
Coordinate System
P2
P3
P0
Initial Angle
0
0
0
Angular Increment
0.6967700
-0.3090170
0.5075677
Radius(pixel)
170
150
180
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.21 (12,000,000 iterations)
Table: Case 3-4.22 Parameters Assigned (Figure 3-4.22)
Point
P1
P2
P3
Coordinate System
P2
P3
P0
Initial Angle
0
0
0
Angular Increment
0.3967700
-0.3390170
0.5075677
Radius(pixel)
170
50
180
Radius Increment
None
None
None
* Positive angle means clockwise rotation, negative counterclockwise.
[Enlarge the image]
Figure 3-4.22 (12,000,000 iterations)

 

CONTENTS:

Index
Introduction
Methodology
Case Study of Aesthetic Forms
 Conclusions