Johannes Kepler found out, that the quotient of two successive Fibonacci numbers approaches to the Golden Ratio Φ.įigure 3: A Fibonacci spiral which approximates the golden spiral, using Fibonacci sequence square sizes up to 34 (Wikipedia)īut what is the connection of the pentagon, the pentagram, the Fibbonaci Spiral with the human face? These geometric shapes may be useful during the 3d modeling process (they are really simple to create with 3d software application), but in what respect the Golden Ratio is the human face of modeling? To use the Golden Ratio for the human face modeling process we need some more information about the real one. In all of them, the ratio of the longer side to the shorter side is φ. (1)įigure 2: Pentagon and pentagram in relationship to the Golden RatioĪnother shape of the human face with a close connection to the Golden Ratio is the Fibbonaci Spiral. The pentagram includes ten isosceles triangles: five acute and five obtuse isosceles triangles. Also, the ratio of the length of the shorter segment to the segment bounded by the 2 intersecting edges (a side of the pentagon in the pentagram’s center) is Φ. Each intersection of edges sections other edges in the golden ratio. The geometrical figures with the closest relationship to the Golden Ratio and the human face are the pentagon and pentagram. (3)įigure 1: Illustration from Luca Pacioli’s De Divina Proportione applies geometric proportions to the human face. ![]() It shows one of the first drawings of a human face in relation to the Golden Ratio. ✽e Divina Proportione« (About the divine proportions) from Luca Pacioli and illustrated by Leonardo da Vinci is a very famous book about mathematical and artistic proportions. Not only mathematicians but also artists discovered the golden ratio as an important tool for harmonious and aesthetic divisions in pictures, statues and buildings. By subtracting the shorter of the two distances from the longer the result is an even shorter distance a-b with the distance to the turn in the ratio b of the Golden Ratio Φ. This property is an example of self-similarity. ![]() ![]() This means that the bigger acts to smaller one as the sum of the two to the larger ones. The ratio divides a line into two parts with (a) 61,8% and 38,2 %. The number is the result of the following equation: The Golden Ratio is an irrational mathematic constant which has fascinated mathematicians in ancient Greece at least 2,500 years ago. Downloadĭownload this paper as PDF: The Golden Ratio in 3D Face Modellingĭownload the MAX (2010) File: PhiMask 1. The ideal of human beauty is not absolute, but comes out of the relationship of individual parts. This pattern should also not be applied to extravagant or comic styled characters. The female pattern of the Phi Mask is an approximation of a masculinized Caucasian female picture, given by the general public that strongly and overwhelmingly prefers above average facial femininity in women (2). But the mask is not an ideal pattern for all character types, including non-European and sub-Saharan or East Asians. Many designers and cosmetic surgeons have found his mask convincing. He claims it represents the ideal facial archetype. Marquardt of the Loma Linda University and the University of Southern California (1). ![]() The pattern we construct in 3D is the Phi Mask (or Golden Mask) of Dr. In this paper I will describe some application possibilities of the Golden Ratio during the 3D modeling process, regardless of the used 3d software.Necessary for the application of this workaround is a semi-complete mesh scan or something else to which the templates of the Golden Ratio can be applied. An important role plays the famous Golden Ratio, which is difficult to be applied in many ways. A problem during the modeling process of real, human-like characters is the observance of certain natural proportions. The freehand modeling of three-dimensional human faces with an usual 3D-animation software is still a big challenge for many CG Artists.
0 Comments
Leave a Reply. |