7. Build a human body using golden ratio and suggested algorithm

This section presents two suggested algorithms that calculate all 35 measurements of the human model. The first algorithm shown in Figure 9 where the input needed is the value of M16. The second algorithm also provides the model with 35 measurements according to golden ratio rules, with the input of the algorithm is the total height of the model. The author experimented with both algorithms and reflected the results in Tables 2 and 3. Furthermore, the results are shown on the model in Figure 12. The first suggested algorithm is explained next.

To build a human model according to the golden ratio using the rules explained above and suggested in Figure 6 Bauentwurfslehre by Ernst Neufert, two algorithms are devised in Figures 9 and 10 that would position the rules as shown next.

First, enter the one basic measurement which is M16 (the length from bottom of feet to ankle). Using the fact implied by formula (1) which is previously explained. Then M17 can be calculated by setting M17 = M16 � 1.61803398874989. Once M17 is calculated, then M7 can be easily determined by using the previously explained formula (2). Furthermore, M8 can be calculated since such fact was established by formula (3).

Hence, M8 = M7 � 1.61803398874989 based on (3). Based on (4), M3 is M3 = M7 + M8. Based on (5), M19 = M18 � 1.61803398874989. Based on (6), M9 = M18 + M19. Based on (7), M21 = M20 � 1.61803398874989. According to (8) M11 = M20 + M21, and according to (9) M4 = M9 + M11, hence and using (10), M4 = M3 � 1.61803398874989. Based on (11) M1 is M1 = M3 + M4, and based on (12) M1 = M2 � 1.61803398874989. According to (13) M2 = M6 + M5, again apply (14) M2 = M5 � 1.61803398874989 and (15) M6 = M2/1.61803398874989. By using (17) and (18) M15 = M6 � 1.61803398874989. Hence, M14 = M6/1.61803398874989; according to (19) M5 = M12 + M13, further according to (20), M12 = M5/1.61803398874989 and based on (21) M13 = M5/2.61803398874989. Based on (22), M12 = M23 + M22 hence M22 = M12/ 1.61803398874989 and based on (24), M23 = M12/2.61803398874989. Based on (25), M15 = M27 + M26 hence based on (26), M26 = M15/1.61803398874989 and based on (27), M27 = M15/2.61803398874989. According to (28) and the use of (29) and (30), M24 = M14/ 1.61803398874989 and M25 = M14/2.61803398874989. Again, according to (31) and the use of (32) and (33), M29 = M24/1.61803398874989 and M29 = M24 / 2.61803398874989.

Another version of the algorithm can be suggested when the total height is given, as illustrated in Figure 10. The author used a simple Microsoft Excel sheet to calculate the rest by applying the same rules seen in Table 2. In order to illustrate the process clearly, an example was set with original value of M16 = 6.13057 cm. To show the results of these simple calculations, the


Table 2. All M's calculated using Microsoft excel sheet.

the figure to the first knuckles (distal phalange) is proportional to the second knuckle (middle phalange) 1: φ, which is equally similar to middle finger, ring finger, and little finger. The thumb from the tip to the (distal phalange) proportional to the proximal phalange is 1: φ and

This section presents two suggested algorithms that calculate all 35 measurements of the human model. The first algorithm shown in Figure 9 where the input needed is the value of M16. The second algorithm also provides the model with 35 measurements according to golden ratio rules, with the input of the algorithm is the total height of the model. The author experimented with both algorithms and reflected the results in Tables 2 and 3. Furthermore, the results are shown

To build a human model according to the golden ratio using the rules explained above and suggested in Figure 6 Bauentwurfslehre by Ernst Neufert, two algorithms are devised in

First, enter the one basic measurement which is M16 (the length from bottom of feet to ankle). Using the fact implied by formula (1) which is previously explained. Then M17 can be calculated by setting M17 = M16 � 1.61803398874989. Once M17 is calculated, then M7 can be easily determined by using the previously explained formula (2). Furthermore, M8 can be calculated

Hence, M8 = M7 � 1.61803398874989 based on (3). Based on (4), M3 is M3 = M7 + M8. Based on (5), M19 = M18 � 1.61803398874989. Based on (6), M9 = M18 + M19. Based on (7), M21 = M20 � 1.61803398874989. According to (8) M11 = M20 + M21, and according to (9) M4 = M9 + M11, hence and using (10), M4 = M3 � 1.61803398874989. Based on (11) M1 is M1 = M3 + M4, and based on (12) M1 = M2 � 1.61803398874989. According to (13) M2 = M6 + M5, again apply (14) M2 = M5 � 1.61803398874989 and (15) M6 = M2/1.61803398874989. By using (17) and (18) M15 = M6 � 1.61803398874989. Hence, M14 = M6/1.61803398874989; according to (19) M5 = M12 + M13, further according to (20), M12 = M5/1.61803398874989 and based on (21) M13 = M5/2.61803398874989. Based on (22), M12 = M23 + M22 hence M22 = M12/ 1.61803398874989 and based on (24), M23 = M12/2.61803398874989. Based on (25), M15 = M27 + M26 hence based on (26), M26 = M15/1.61803398874989 and based on (27), M27 = M15/2.61803398874989. According to (28) and the use of (29) and (30), M24 = M14/ 1.61803398874989 and M25 = M14/2.61803398874989. Again, according to (31) and the use of

(32) and (33), M29 = M24/1.61803398874989 and M29 = M24 / 2.61803398874989.

Another version of the algorithm can be suggested when the total height is given, as illustrated in Figure 10. The author used a simple Microsoft Excel sheet to calculate the rest by applying the same rules seen in Table 2. In order to illustrate the process clearly, an example was set with original value of M16 = 6.13057 cm. To show the results of these simple calculations, the

7. Build a human body using golden ratio and suggested algorithm

on the model in Figure 12. The first suggested algorithm is explained next.

Figures 9 and 10 that would position the rules as shown next.

since such fact was established by formula (3).

to the joint connecting the hand is 1: φ 2 as shown in Figure 10.

130 Machine Learning and Biometrics


numbers were reflected on the same Figure 10, while it is worth noting that some interesting facts were realized and seen in Table 2 as follows: first, M28 and M26 are equal to each other; second, M16, M25, M27, M29 are equal; and third, M15, M17, M18, M23, M24 are equal. Again, M7, M13, M14, M19, M20, M22 are all equal to each other. In addition, M21, M8, M9, M6, M12 are equal to M8 are equal to each other. And M3, M5, and M11 are equal to each other. Finally, M4 and M2 are equal to each other. Hence, the suggested algorithm can be done with mini-

A Human Body Mathematical Model Biometric Using Golden Ratio: A New Algorithm

http://dx.doi.org/10.5772/intechopen.76113

133

To build a human body using proportions suggested by Vitruvian Man discussed in the earlier section, then the height intended for the human figure should be designated first (shown in Figure 12). As illustrated by Table 3, the height entered was 178 cm, whereby using simple

The goal of this chapter was to enable a multimedia modeler to model a human body using the golden ratio. Hence, the research uncovers 35 measures based on golden ratio introduced by Bauentwurfslehre by Ernst Neufert (1936) and Vitruvian Man (The Man in Action) by Leonardo da Vinci. The 67 measurements are: feet bottom to navel, navel to top of head, feet bottom to knee bottom line, knee bottom line to navel, navel to pit of throat & elbow to tip of the shoulder, pit of throat to top of head, bottom of feet to begin of calves, from calves to bottom line of knee, bottom line of knee to mid thighs (beginning of finger tips), mid thighs (beginning of finger tips) to navel, navel to middle of chest, middle of chest to pit of throat, pit of throat to point between the eyes, point between the eyes to top of head, bottom of foot to ankle, ankle to beginning of calves, beginning of knees to end of knees, top of knees to tip of hand fingers (hand toward earth), hand tip of fingers to hand rest, hand rest to elbow and navel to man gentiles, navel to beginning of chest (abdomen), beginning of chest to middle of chest, throat pit to below nose, blow nose to top of eyebrows, top of eyebrows to hair line, hair line to top of head, from throat pit to Adam's apple, Adam's apple to below the nose, the length of the face = M25 + M26 + M29, width of the face = length of face/1.618, left tip of eyebrow to the right tip of eyebrow = M25 � 1.618, from tip of eyebrow to between the eyes = 2 � M25/1.618, width of shoulders 1/4 of height of a man, foot is 1/6 of the height of a man. The measurements are based on 25 proportional rules derived from 15 proportions given by Vitruvian Man and 29

First, the chapter explained the golden section (mathematically, geometrically, arithmetically), then further demonstrated the golden ratio with phi. Furthermore, the chapter discussed Vitruvian Man (The Man in Action) by Leonardo da Vinci. Furthermore, explained Bauentwurfslehre by Ernst Neufert. The chapter, then, proposed how to build a human model using the ratios explained and proposed two algorithms that a modeler can follow to build a human body. The algorithms output can be used as proportions and an integral part of design and beauty of nature, to achieve beauty, balance, and harmony, thereby presenting visual parity serving guideline to human body modelers in simulation, gaming, plastic surgery, as well as the world of biometrics or wherever human body measurements and calculations is needed

mum line of code as shown in Figure 8:

8. Conclusion

calculations, the results are shown in Table 3.

golden proportions in Bauentwurfslehre by Ernst Neufert.

Figure 12. Bauentwurfslehre by Ernst Neufert [14] with heights reflected in centimeters with a base number M16 = 6.1305.

numbers were reflected on the same Figure 10, while it is worth noting that some interesting facts were realized and seen in Table 2 as follows: first, M28 and M26 are equal to each other; second, M16, M25, M27, M29 are equal; and third, M15, M17, M18, M23, M24 are equal. Again, M7, M13, M14, M19, M20, M22 are all equal to each other. In addition, M21, M8, M9, M6, M12 are equal to M8 are equal to each other. And M3, M5, and M11 are equal to each other. Finally, M4 and M2 are equal to each other. Hence, the suggested algorithm can be done with minimum line of code as shown in Figure 8:

To build a human body using proportions suggested by Vitruvian Man discussed in the earlier section, then the height intended for the human figure should be designated first (shown in Figure 12). As illustrated by Table 3, the height entered was 178 cm, whereby using simple calculations, the results are shown in Table 3.
