Parametric design for custom-fit eyewear frames

Abstract

More than half of the people on the planet use eyewear to correct or protect their vision. Eyewear products that fit poorly cause discomfort, dizziness, or blurred vision. One method to improve fit is to create custom-fit eyewear frames on an individual basis. In this paper we propose a new parametric design method to customize the eyewear frames based on individual 3D scanned data of head-and-face measurements. We take the eyeglasses frame as the case study to establish the landmark-product relationship and develop the parametric algorithm in Rhino/Grasshopper software. The results of the case study can generate custom-fitted eyeglass frame models for the two selected subjects, one 33% percentile Asian female and one 90% percentile Caucasian male. The future study will continue validating the eyewear frame fit and optimizing the parametric design method.

1. Introduction

Over half of the adult population of the world use prescription eyewear to protect or correct their vision. People wear glasses to safely navigate their environment and for specialized tasks like driving or reading. Invented in the 13th century [1], eyewear products have evolved into essential daily-use consumer goods. Well-fitted eyewear improves the quality of the wearers' lives by bringing the world into sharper focus and correcting the degraded vision caused by aging, but poorly fitting eyewear causes discomfort, dizziness, and blurred vision [2]. Our study addresses the prescription eyewear design process and does not include the design of off-the-shelf sunglasses.

Today's eyewear industry is a massive business that produces a variety of styles, shapes, and sizes for its customers across the globe. Designing prescription eyewear starts with a multi-step optical examination to prescribe the right corrective lenses for a person's vision. This is followed by a try-on session to find the eyeglass frame that best fits the subject's face. The optician then assembles the corrective prescription lenses into the frame and uses a frame warmer to make fit adjustments like bending the frame arms to lengthen them or altering the angle of the frame to better fit the customer's face. The vision is checked one last time with the adjusted frame and the process is complete.

Most of the current eyeglass frames are designed using a proportional grading or scaling approach based on interpupillary distance in correlation with face width and temple length [3]. This traditional design method fails to address the full diversity of human face morphology.

Human face morphology varies widely according to ancestry, age, and gender. In Marcha and Angus's study on evaluating and designing eyewear fit for South African populations, their results showed that both “Asian fit” and “Regular fit” eyewear frames were not suited to the facial structures of the South African population [4]. In addition to variations in populations, the diversity among individuals can also result in a poor fit. Critically, the rigid proportion or correlation approach does not always account for individual facial shapes. For example, a person with a wide face but a narrow nose bridge will not achieve a proper fit with these pre-defined sizes. Outliers with extreme head-and-face morphologies fall outside of the current eyeglasses market.

With the rising awareness of these fit-related problems, design researchers have been exploring new solutions to offer better-fitting eyewear. One solution for improved fit is to offer customized eyeglasses frames on an individual basis. In this paper, we propose a new parametric design method for creating custom eyeglass frames using 3D face scanning, parametric design method, and additive manufacturing.

2. Anthropometric study

Designing custom eyewear requires a working knowledge of the relationship between the anthropometry of the head and face and eyewear design methods. The shape or morphology of the human face is difficult to measure because its organic geometry lacks straight lines, right angles, or convenient measuring planes. The proposed design method establishes a set of facial landmarks that are used to generate a custom frame using a 3D parametric model and CAD software. Using the facial landmarks, a designer manually positions the parametric frame model on the underlying face scan to begin the design process. Once the parametric frame is positioned on the head scan the coordinate values of the landmarks are then extracted from the scan and entered directly into the stretchable parametric frame model and the custom design is generated. The finished CAD file is then exported to a 3D printer to create the custom eyeglass frame.

2.1. Landmark research

In the past decades, many studies have been exploring the solutions to better-fitted eyewear from an anthropometric point of view. These studies provided some vital landmarks on the face and head for designing different types of eyewear products. In 2004 Japanese researchers proposed a set of facial landmarks for wearable product design based on the CAESAR database [5]. In 2017 Chu proposed a method to create personalized eyeglass frames based on 12 parameters extracted from a 3D face scan [6]. Another study of three-dimensional human face morphologies in 2010 provided 47 landmarks for proper spectacle frame sizing, particularly involving the complex rear-ear points [3]. In 2021 Bai created formulas between 12 eyeglass design parameters and 18 facial features for improving the design of eyeglasses [7].

2.2. Landmark development

Based on the preliminary landmark research, we identified 32 primary facial landmarks to develop the final parametric eyeglass frame model. 26 points out of the 32 landmarks can be identified and marked (with eyeliner pencil) through palpation or visual inspection prior to the 3D scan. The rest 6 landmarks including pupils and eye orbit points are not safe for physical marking and were virtually marked on textured scan data files. The following Fig. 1 lists the 32 primary facial landmarks needed for parametric design.

Fig. 1.

Primary facial landmarks for parametric eyewear design.

In addition to the 32 primary facial landmarks, 10 secondary dimensions including distances, contours, and angle values are required to further establish the relationship between the face shape and the eyeglass frame components, as shown in Fig. 2. The primary landmarks and secondary dimensions can be digitally extracted from a high-resolution 3D face scan using Rhino [8] and Grasshopper software [9]. These univariate landmark coordinates and dimension values are entered in the stretchable parametric eye frame model by manually selecting points in Rhino or inputting the number values.

Fig. 2.

Facial dimensions for eyewear design and body-product relationship establishment.

3. Eyewear design

3.1. Eyewear frame components

An eyewear frame is comprised of a set of components, the front frames, the lens cavities, the hinge (between frames and arms), the two arms, and the nose bridge. Designing a customized eyeglass frame requires establishing the body-product relationship between the facial landmarks and the eyewear components. The eyewear frame dimensions can be calculated using numerical formulas and geometric relations based on facial landmarks and dimensions [5]. In addition to the basic relationships that determine the frame size, nose bridge size, and arm size, we applied other fit elements [10,11,12] that can help adjust the face wrap, pantoscopic tilt, vertex distances, nose bridge curvature, and ear hang curvatures on the arms using our extracted dimensions. The following image illustrates the eyewear frame components in Fig. 3. Each part contains its related components annotated in uppercase alphabet letters corresponding to the lowercase annotations in Fig. 2.

Fig. 3.

Eyeglasses components and a glossary of eyewear design terms.

3.2. Fit factors

Achieving a good fit in eyewear design requires understanding the physical fit factors. Four fit factors that need to be satisfied in eyewear design are quantitative fit, contact fit, interference fit, and ventilated fit. Analyzing these fit factors can help us “decompose” the eyewear components and establish a proper Body-product relationship.

Quantitative fit ensures the appropriate size by regulating the product dimension to coordinate with certain body measurements. It refers that the dimension of the product should be controlled within a measured range among certain landmarks or ruled by certain geometrical equations. A typical quantitative fit in an eyewear case is the front frame length (half as an example) being larger than the eye orbit length while not exceeding the temple area. Or, the face wrap and pantoscopic tilt should align with the facial curvature by correct angles.

Contact fit describes the interface of the hard surface of the eyewear frame with the soft surface of the wearer's skin. Contact fit is used when the surface of the front frame needs to rest lightly on the surface of the wearer's skin. The nose bridge is the critical area for contact fit in eyewear. In this case, the nose bridge contours should conform to the user's nose bridge shape represented by two nasal root points (3&4) and the sellion point (0).

Interference fit is required so that the arms of the eye frame can grip the side of the head above the ear to prevent it from falling off the face when looking down or quickly moving the head. Taking facial landmarks as a basis, interference fit uses slight adjustments to provide an extra constraining allowance for tightened fit.

Ventilated fit is required to create spaces for the free movement of air between the wearer's face and the eyewear frame. Ventilated fit is required to ensure the wearer's eyelashes don't contact the lenses and have room to move freely. Ventilated fit also dissipates any localized heat buildup that can lead to lens fogging. The vertex distance is a typical ventilated fit for eyewear design.

3.3. Body-product relationship

Analyzing the fit factors helps us “decompose” the eyewear into components and establish a framework for body-product relationship. The body-product relationship develops a guideline of equations, correlations, and necessary tolerances between the body landmarks and the product dimensions. Some of the components, except for controlled by body-product relationship, are also designed to be adjustable for achieving customized comfort, function, and styles by setting adjustive parameters. In this section we will focus on interpreting the body-product relationship and discuss the details of these adjustive parameters in the next section.

3.3.1. Front frame positioning

The first step is to confirm the proper position of the front frame. The front frame positioning refers to the overall front surface that contains the frame edges, lenses, nose bridge, and two hinges. Due to the complexity of fit, the frame shape, nose bridge, and hinges are treated as separate components in the following sections. In this section, we mainly discuss the face wrap, pantoscopic tilt, and vertex distance. These components determine the initial positioning of the eyeglasses frame for proper wearing. For example, the front frame should conform to the user's face curvature profile yet keep a proper distance from the pupils and allow free movement of the wearer's eyelashes.

3.3.1.1. Face wrap

The face wrap describes the horizontal angle of the frame and lens surface in front of the face [12]. The face wrap is dependent on the style of the parametric frame. For a wraparound sunglass style, the face wrap is as close to the face as comfort allows to achieve the “aerodynamic” aesthetic whereas in a Harry Potter style the face wrap is located some distance from the face to achieve the “nerdy” style. Most prescription eyeglasses frames follow a standardized face wrap angle range from 0 to 10° while the sunglasses range from 12 to 25° [12]. In this study, the face wrap can be customized to conform to the individual's facial curvature. The forehead curve (a) through the Eyebrow lateral points (17&18) and the Glabella (1) are used to construct the curved front surface of the frame. We can calculate the angle between the forehead curve (a) and the horizontal line. In our algorithm, the default of halved angle between the horizontal line and the Forehead contour (a) is settled as the front surface curvature, as shown in Fig. 4(a). Both front frames and lenses should be constructed onto this curved surface with the same face wrap.

Fig. 4.

Positioning the eyewear frame using Face wrap, Pantoscopic tilt, Front surface, and Vertex distance. (a). Extracting the Forehead contour (a) from connecting Glabella (1) and both Eyebrow Lateral points (17&18). Construct the Face Wrap contour (A) using the halved angle. (b). Constructing pantoscopic tilt (B) as a referential line using Nasian tilt (b) based on Glabella (1) and Sellion (0). (c). Constructing a curvature surface for face wrap with Face Wrap (A) and Pantoscopic tilt (B). (d). Adjust the distance between face wrap surface and the Pupil (c). The green surface is shifted away from the defaulted red surface.

3.3.1.2. Pantoscopic tilt

The pantoscopic tilt, along with the face wrap, defines the front surface position. While the face wrap determines the front curvature that conforms to the face profile, the pantoscopic tilt mainly describes the gradient of the front frame along the vertical direction [12]. For example, in most cases, the front frame should yield a slight inclination to conform to the tilted facial profile from the upper eyebrow area to the lower face. We use the Nasian tilt (b), a tilted line connecting the Glabella (1) and the Sellion (0) to calculate the pantoscopic tilt. By measuring the angle between the reference line and the vertical axis Z, we obtain the pantoscopic angle value the pantoscopic tilt B, shown in Fig. 4(b). With both face wrap and pantoscopic tilt determined, we construct a curved and tilted front surface for reference as shown in Fig. 4(c).

3.3.1.3. Vertex distance

The vertex distance C refers to the distance between the front frame (front surface) and the pupil (7 or c). As we construct the front surface with the face wrap and pantoscopic tilt, we can set an adjustable value range to shift the front surface away from the pupil point within a certain distance. According to our research, the recommended vertex distance can range from 8 to 20 mm [12] with a most common average value of 12 mm [10]. With the face wrap, pantoscopic tilt, and vertex distance confirmed, the proper front frame position is then identified on the front surface, as shown in Fig. 4(d).

3.3.2. Front frame size

The front frame contains two frame cavities on both eyes symmetrically, with two crucial dimensions, the length (D1) and the height (D2), as shown in Fig. 3. Technically, the frame length and height should be correlated to the landmarks around the eye orbit. The frame length should start at the Nasal root point (3) and cover up to the Eyebrow Lateral point (17). The frame height D2, as shown in Fig. 3, is an adjustable dimension that relies on the frame styles. However, the bottom line is that the frame height should cover at least to the Infraorbital (13), up to 2/3 of the nose height as we set for recommended maximal height. Therefore, we identify an auxiliary landmark S2 to indicate the lower point of the frame height by extending the 2/3-point S1 on nasal height, as shown in Fig. 2. The eye orbit (d2) in Fig. 2 demonstrates the referential dimension for frame height. Fig. 5(a) demonstrates the constructions of the eyewear frame contour in the algorithm shown on half side.

Fig. 5.

Eyewear components construction exemplified on half side in parametric modeling. (a). Front frame contour based on related landmarks and dimensions. (b). Hinge added based on Eyebrow Lateral point (17) and Temple point (31). (c). Lens cavity contour by offset adjustive parameters from frame contour. (d). Arm contour based on related hinge point and ear landmarks. (e). Nose pad contour based on Sellion (0), Nasal Root point (3), and adjustive point on frame. (f). Half frame contour constructed and assembled.

3.3.3. Hinge component

The hinge (F) in Fig. 3 is an important component because it provides the connection between the end of the frame edge and the start of the arm and allows the eyewear to be folded when not in use. Taking an example of the front view, the hinge should extend from the frame's outer edge, as known as the Eyebrow Lateral point (17) but not exceed the Temple point (31). As shown in Fig. 2, the hinge dimension (f) demonstrates the location of the hinge component. Furthermore, the hinge component has several adjustive parameters to alter the height, shape, and radius for different styles as discussed in the following section. Fig. 5(b) shows the hinge added to the frame edge contour.

3.3.4. Lens cavity size

Lens cavity (E), as shown in Fig. 3, simply conforms to the same shape, ratio, and proportion of the front frame yet has a smaller grooved interior channel that allows the lenses to snap fit into place. Besides, the lens cavity must cover both Ectocanthion (9) and Ectocanthus (11) to provide a full coverage for eyesight. In Fig. 2, the eye length (e) indicates the minimal size of the lens cavity. In the parametric model, the lens cavity is defined by an adjustive parameter that scales down from the frame size while limited by the minimum eye length (e) coverage. Fig. 5(c) shows the lens cavity generation.

3.3.5. Eyeglasses arm

In this eyewear style, we model the arm with a wide “blade” shape arm with a scallop for the ear pinna. We establish the arm length using the Ear Top point UEBP (25/26), Ear Back point IMP (27/28), and Ear Back Middle point PEBP (29/30).

First, the overall arm breadth (G1) requires a relative “snug” fit on the head width to avoid the eyewear slipping off the face when looking down or turning the head rapidly. This means that the distance between the two arms needs to be less than the head breadth (g1) to allow the arms to grip the head. We select the distance between two Ear Top points UEBP (25/26) and adjust the arm dimensions with a smaller negative dimension. This negative dimension allows the arms to grip the top of the ear areas snugly to hold the eyewear in place. In the parametric model, this “grip” function is achieved by shrinking the arm breadth 1–3 mm of the head breadth dimension. Designing a “snug fit” is challenging because each individual wearer will have their own personal opinions about what is the correct amount of pressure for them. The difference between a snug fit and a tight fit may only be a few millimeters but it is crucial to the wearer's daily comfort.

Another aspect that affects comfort is the shape of the rear portion of the arm that contacts the back of the ear. In this parametric model, we use a scalloped contour (G2) based on the curvature of the back ear contour (g2). As shown in Fig. 2, the back ear contour (g2) is extracted from the UEBP (25/26), PEBP (29/30), and IMP (27/28). By interpolating these three points into a smooth curve in the parametric algorithm, we can define and construct the shape of the rear ear hang portion to ensure the conforming contact of the eyewear arms.

Fig. 5(d) demonstrates the arm shape construction in the algorithm shown on side view.

3.3.6. Nose bridge

Finally, the nose bridge contour (H) is a small but crucial component for the fit and comfort of eyeglasses. The nose bridge shape is intended to rest lightly on the sides of the nose creating a contact fit with the skin surface. The nose bridge shape is one of the most problematic fit areas in eyewear design because it is usually designed using the simple univariate dimension of nasal width without considering the 3D morphology of the nose. By using high-resolution face scans, we are able to create an accurate 3-dimensional shape of the nose bridge in the parametric model. The nose bridge contour (h) as shown in Fig. 2 is used to design a morphologically accurate nose bridge shape. The nose bridge contour (h) can be accurately extracted by interpolating both the Nasal root points (3 & 4) and the Sellion point (0). Thus, the nose bridge on eyeglasses is designed to fit all morphologies around the nasal area, not only the width dimension but including the height, shape, and curvature. The parametric model also includes adjustive parameters to fine-tune the nose bridge contours for improved fit. Fig. 5(e) shows the nose bridge contour generated in the algorithm.

To briefly conclude, we deconstruct the eyewear into components and analyze each component with its related facial landmarks to establish the body-product relationship. Some of the relationships are based on a quantitative fit that requires an exact dimension match between the face and the eyewear. We use extracted angles, radians, and distances from scan data to indicate corresponding eyeglasses dimensions. Others involve more complicated geometrical fit factors such as contact fit or interference fit based on the curvature and contour values extracted from each individual face scan. Fig. 5(f) shows the half frame contour generated on the mannequin head model. Beyond this, we also include adjustable parameters to preserve the flexibility of the customization.

3.4. Parametrization for customization

Another important criterion of customization design is to provide adjustability that can cater to the user's unique needs and preferences. As mentioned in the above context, adjustable parameters are utilized for further tuning the product dimensions (e.g., vertex distance, frame height, hinge size, etc.). Two types of parameters work in coordination to accomplish the customization of the eyewear design. The body parameters (landmarks, measurements, and contours) extracted from scan data settle an underlying configuration for proper size and fit. Meanwhile, the adjustive parameters add more attributes to fulfill the comfort, functionality, and aesthetics.

3.4.1. Determine size and fit

The coordinate values of 32 landmarks can be directly imported into the Grasshopper algorithm. The dimensions among landmarks and curve lengths can also be calculated in Grasshopper processors. The spatial relative positions and measurements among all landmarks vary from person to person due to the variety of facial structures. According to the body-product relationship, the defaulted structure of the eyewear frames is constructed based on the imported landmark coordinates by connecting paired points or interpolating through multiple points as identified in Fig. 2, Fig. 3. Because of the different layouts of landmarks for different facial profiles, the overall size and proportion of the eyewear structure can alter dramatically once a new set of landmarks is acquired. Before any manual adjustments, the eyewear frame structures are automatically formed based on the body parameters of the 32 landmarks and their derived measurements. The following Fig. 6(a) display the body parameters entered in the parametric algorithm; Fig. 6(b) demonstrates the eyewear structure with correct size and fit but without adjustive parameters tuned.

Fig. 6.

Body parameters are entered in the algorithm to generate a correct size and fit. (a). Body parameters: The landmarks are acquired as point coordinates with exampled Pupil point (7) highlighted in green. The dimensions (three examples showed) can be either extracted in algorithm by computing the distance between two points, or manually entered the numerical values after digitally measured in Rhino, as shown in yellow panel notes. (b). The defaulted eyewear frame structure in customized size and proportions only after the body parameters are entered, with adjustive parameter values settled as default or clear (e.g., zero radius for edge fillet).

3.4.2. Affecting comfort and function

As the body landmarks define the defaulted size and proportion of the eyewear, adjustive parameters can further affect the comfort level and ensure the correct functions related to ventilated fit and interference fit. The comfort and functionality are not treated strictly separately but can mutually affect each other for several components.

The vertex distance, considered a ventilated fit factor, is an important element that affects both comfort and function. The front frame being too close to the face may irritate eyelashes and facial skin, while being too far can cause vision correction malfunction. Therefore, we set a numerical slider to shift the front frame within a range of recommended 8–20 mm away from the pupils. With this adjustment, the eyewear frame can provide flexible space for different wearing habits.

The arm breadth, considered an interference fit factor, also needs to be adjusted comfortably based on personal preferences as well as maintain the function of grabbing the head securely. Based on the landmarks around the ear, the arm is constructed exactly to sit on the scan data (skin surface) which in the real world can become loose and cause slide-off. In the parametric algorithm, we add a small-scaled number slider to shift the arm inwards within 3 mm to guarantee the gripping function. At the same time, if needed, this value can change precisely for a trial-and-error process to adapt to a most satisfied tightness level for individual users.

The following images in Fig. 7 shows two different settings of Vertex Distance and Arm Breadth. Fig. 7(a) demonstrates that both values are settled as minimal and 7(b) demonstrates the adjustments of moderate value for Vertex Distance and maximal value for Arm Breadth.

Fig. 7.

Adjustive parameters of Vertex Distance and Arm Breadth are set differently for comfort and functionalities. (a). Adjustive Parameters of Vertex Distance and Arm Breadth are settled as minimum values. The front frame tightly sits on face with a distance to pupil at 8 mm; the two arms are shrunk inwards 1 mm slightly sit on scan data. (b). Adjustive Parameters of Vertex Distance and Arm Breadth are settled as moderate and maximum values respectively. The front frame is in moderate distance to pupil at approximately 14 mm; The two arms are shrunk inwards 3 mm which can grab the head more tightly.

Another adjustive parameter is settled for the most problematic component, the nose pad. Despite the nose bridge contour being regulated by the nasal landmarks by default to achieve a contact fit, the parametric design provides additional features for curves. By selecting different curve types and tuning the control points, the nose pad curvature and size can be altered delicately, as shown in Fig. 8. In panels 8(a),(b), and (c), the green-highlighted Nose Pad Contour is individually selected as Uniform, Chord, and SQRT curve types. This feature can provide different adaptions on users’ perceived comfortableness regarding the depth, tightness, and sharpness of the nose pad area.

Fig. 8.

Adjustive parameter of Nose Pad contour can be fine-tuned to achieve different nose bridge comfortableness. (a). Adjustive parameters of Nose Pad contour is settled as uniform curve type which interpolates exactly on landmarks with no other factor added. (b). Adjustive parameters of Nose Pad contour are settled as chord curve type with a stretch factor to provide a relatively shallower contour for relaxed fit. (c). Adjustive parameters of Nose Pad contour are settled as SQRT curve type with a stretch factor to provide a relatively deeper contour for tight fit.

3.4.3. Tailoring for aesthetics and styles

Lastly, to meet the various tastes of aesthetics and styles is a considerable demand for customization design. Even within a classic rectangular-shaped eyewear frame, we can encode many adjustive parameters to adjust the appearances to a certain degree.

On the premise of guaranteeing the proper fit, we add the major styling elements on the frame component including the lens cavities and hinge parts. The frame height can be extended lower to keep up with the fashion trend of “oversized lenses”; The center bridge between the two frames is stretchable from straight to arch, carrying both sleek and organic styles; The lens size can be scaled within the frame shape from a slim-edged style to a thick-edged style. Accordingly, both the frame and lens radius are adjustable with numerical value sliders. Finally, the hinge part contributes to the style variations by adjustable height, length, and radius as well. The following images in Fig. 9 (a)(c) demonstrate the adjustive parameters for styling elements on the front frame.

Fig. 9.

Adjustive parameters for Front Frame and Arm style elements. (a). Front frame narrow and slim style, center bridge arched, small edge radius, narrow and slim hinge parts. (b). Slim arm style with small blade shape factor. (c). Front frame oversized and bulky style, center bridge more straightened, large edge radius, wide hinge parts. (d). Wide arm style with large blade shape factor.

Other adjustive parameters are placed on the arm design. The arm height controls the vertical dimension which offers both a slim and a wide design. The “blade” shaped arm is one of the classic features of many modern eyeglasses. In the algorithm, we use a “point on curve” parameter to locate the “blade” shape on different positions. Besides, the radius of the upper, lower, and end corners on the arms can be tuned. The following images in Fig. 9 (b) (d) demonstrate the styling elements on arm.

4. Parametric model development

Rhino 3D software with Grasshopper plug-in offers a powerful tool to construct 3-dimensional geometries of parametrization. Fig. 10 displays a general layout of the Rhino/Grasshopper Parametric design platform. The left side is the Rhino displayer for model visualization while the right side is the Grasshopper program for algorithm design, as shown in Fig. 10(a). Fig. 10(b) displays the layout of the Grasshopper coding interface containing different blocks of eyewear component constructions.

Fig. 10.

A global view of parametric design algorithm demonstrated on the mannequin model. (a). The layout of parametric design is composed of Rhino CAD software for visualizing design variations on the left side, and Grasshopper interface for coding the parametric algorithm and adjusting parameters on right side. (b). The layout of the parametric algorithm in the Grasshopper coding interface. Each block encodes its processors (batteries) for constructing eyewear components.

The Grasshopper program provides multiple “battery” shaped processors for bridging the numerical, geometrical, and logistical relationships. In the algorithm, each color block contains the algorithm with multiple battery processors that constructs one component or part for the eyewear structure. Fig. 11(a) shows the algorithm block that constructs eyewear front frames, hinges, and lens cavity. Fig. 11(b) and (c) shows the blocks that construct Arm and Nose Bridge, respectively. Fig. 11(d) shows the final integration block all components into the completed eyewear wireframe.

Fig. 11.

Local views of each block containing processors in parametric design algorithm. (a). Parametric processors (algorithm) for front frame, hinge, and lens cavity. (b). Parametric processors (algorithm) for Arm. (c). Parametric processors (algorithm) for Nose bridge. (d). Parametric processors (algorithm) for the entire frame union.

Despite the product-landmark relationship clarifying the product components and facial profiles clearly, the actual parametric algorithm in Grasshopper is weaved in a more complex manner. We should note that the landmarks and dimension values are NOT one-to-one connected to each battery processor instead they are developed as an interactive network where a single value is linked with several batteries. Or multiple values are affecting a single battery in coordination. For example, the Temple point (31), the Temple point serves as the stopping indicator for the hinge on the front view, as well as the starting point for the arm on the side view. This means that the Temple point coordinate value is used twice in both hinge and arm battery groups.

In the algorithm, we design the eyewear by using the right side of the face to begin with. Once the frame design has fitted to the scan data on the right side, the model is given an extensive visual examination using zoom and rotate functions to view every part of the interface between the face scan and the custom model. After micro-adjustments to the right side then the mirror and duplicate functions allow us to complete the whole eyewear frame as a symmetrical structure.

This parametric design method generates a customized eyeglasses frame. Each completed design is saved into the Rhino 3D displayer as an editable 3D model. Due to the heavy load of computation to generate a solid model in Grasshopper, we keep the frame wireframe structure as the final step in the parametric model and manually process the solid modeling process in Rhino software for efficiency.

5. Pilot test

5.1. Subject data collection

We recruited two adult subjects within the research team for a pilot test for 3D scanning and algorithmic eyewear generating. Prior to the scanning process, the subjects' head and face landmarks were identified through palpation and the location was marked using an eyeliner pencil.

The subjects were fitted with wig caps to reduce the effect of hair noises. Post-processing of the scan removed scan noise, aligned the scan, and filled small holes in the surface. The face scan file is then imported into the CAD software and assigned its own layer.

To test as much diversity of facial morphology as possible, we select two subjects with largely different head-and-facial profiles. One subject is a Caucasian male with a head circumference of 62 cm, accounting for the 97% percentile referencing to the CAESAR database [13,14]. Another subject is an Asian female with a head circumference of 54 cm, at 33% according to the Size China database [15]. At this early stage of the study, the two subjects represent two distinct head and face shapes and a large size range difference between them. The following images in Fig. 12(a) and (b) document the anthropometric data for Subject A and B respectively.

Fig. 12.

Anthropometric data (landmarks and dimensions) for two subjects on scan data. (a). Front view of landmarks and dimensions for Subject A. (b). Side view of landmarks and dimensions for Subject A. (c). Top view of landmarks and dimensions for Subject A. (d). Front view of landmarks and dimensions for Subject B. (e). Side view of landmarks and dimensions for Subject B. (f). Top view of landmarks and dimensions for Subject B.

5.2. Parametric model generation

The final step before generating the custom design is to extract and assign the landmarks in the Rhino and Grasshopper program. These univariate values are entered into the parametric model and the custom design is generated. The resultant wireframe eyewear frames are then visually inspected with final micro adjustments and then transferred into Rhino software for final CAD modeling. Fig. 13(a) shows the eyewear frame result for Subject A while 13(b) shows the result for Subject B.

Fig. 13.

The generated parametric eyewear wireframes shown on the two subject face scans. (a). Parametric design outcome of eyewear wireframe for Subject A, a Caucasian male with a head circumference of 62 cm, at 97% as a percentile based on the CAESAR database. (b). Parametric design outcome of eyewear wireframe for Subject B, an Asian female with a head circumference of 54 cm, at 33% as a percentile based on SizeChina database.

5.3. CAD modeling finalization

Due to the heavy computation workload in generating solid models in the Grasshopper program, the CAD models for both subjects are completed after the customized eyeglasses wireframes are generated. This step requires modeling the wireframes into a watertight solid CAD file that can be prototyped (e.g, for 3D printing). In Rhino software, we manually patch the surface based on the wireframe structures and extrude the surfaces into solid with 3 mm thickness. Fig. 14 (a) and (b) displays the solid CAD models for Subject A and B respectively.

Fig. 14.

Completed CAD eyewear frame 3D models for two subjects. (a). Final CAD modeling and rendering of parametric eyewear frame for subject A. (b). Final CAD modeling and rendering of parametric eyewear frame for subject B.

6. Discussion

6.1. Potentials and contributions

The parametric design method for custom eyeglass frames enables designers and engineers to create better-fitting eyewear for any head shape or facial profile. Compared to the mass-produced eyeglasses that are pre-defined with certain size segmentations, the parametrized eyeglasses frames are capable to fit a larger range of populations, not only on head sizes but also conform to individual facial contours and cater to individual demands. Potentially, the complexity of face and head variations among populations and demographic factors can be improved for eyewear fit. The poor fit problems for outliers outside of the traditional industry sizing, with extreme head sizes or facial features, can also be resolved with the capability of parametric design models.

6.1.1. Eyewear design varieties

In this study, we chose a common and classic eyewear type of “rectangular-shaped” frame as an exemplified case to experiment with the parametric design method. The result showed that the parametric design method can be utilized to achieve the customization with the 3D scan technology and anthropometric knowledge involved. In this particular case, the frame profile is constructed from selected landmarks around the eye orbit and interpolated into a rounded rectangle shape. However, chances exist that other types of eyewear can also be created through parametric design if other appropriate landmarks are identified and correct geometric correlations are established. For example, the round-shaped frame could be constructed using the pupil point as centroid, with proper values (e.g., larger than eye orbit but smaller than nasal-temple distance) to adjust diameters for lens size. For a more complicated example such as a cat-eye shaped frame, is also feasible to be customized by lowering the frame inner edge from the eyebrow medial point and raising the outer edge from the temple point. This being said, different types of eyewear products require establishing different body-product relationship and setting different parameters for adjustability. However, the underlying logic of building geometrics upon anthropometric data can work universally for customization and parametric design. Ideally, we can synthesize several parametric algorithms into one comprehensive system in which choosing the desired eyewear type initiates the corresponding built-in algorithm for further customization.

6.1.2. A new method for custom-fit wearable product design

Beyond the eyeglass frames, the parametric design method has the potential to be applied to multiple body fit products. The biggest challenge for designers and engineers is to establish the body-product relationship at the outset of a project. This parametric design method allows designers to “deconstruct” and “reconstruct” the product fit components based on a wearer's individual body morphological scan data and key body fit landmarks. Using this parametric approach method, designers can encode the body-product relationship into a parametric algorithm. Rhino/Grasshopper provides a relatively easy and straightforward platform to fulfill the parametrization and algorithm design. To designers, this method develops a groundbreaking path for designing better-fit wearable products with an improved fit for any body shape.

Many types of wearable products based on custom-fit design can be developed with the parametric design method. Each category of body fit products has its own specialized functions and performance requirements. From medical respirators and PPE (personal protective equipment) smartwatches to AR/VR headsets and smartwatches, all body-fit products seek to provide the optimal fit for individual body morphologies to improve product performance. The parametric design method can be quickly integrated into best practices product design workflows with a 3D digital design environment.

6.1.3. A broad vision towards Mass Customization

The concept of Mass Customization emerges rapidly in recent decades, along with the advancing technologies and expanding customer needs. An essential characteristic of Mass Customization is the idea of “Co-creation” or “Collaborative Design” [16]. It involves customers’ participation in the product design phase. Besides, the blooming E-commerce provides online platforms for Collaborative Design environment [17]. Our proposed parametric design method can be viewed as a frontier attempt to achieve “Collaborative Design” in a more effective and efficient way. By packing the parametric algorithm into an interactive interface, users are able to play with the parameters while visualizing the real-time product variations. Taking the custom-fit eyewear as an example, it is feasible to build up a front-to-end service that faces to the customers based on a fully-integrated parametric algorithm. This service journeys from the user uploading a personal image or 3D data, using online service to customize their eyewear frames, and placing the order for manufacture, and ultimately receiving their purchased products.

The efficiency, dynamism, and interactivity of the parametric design bridge the long-existing seams between designers and customers. It provides a straightforward, learnable, and highly flexible tool for both designers and customers to accomplish the customization. A broader vision from this study implies that the parametric design method can contribute to and apply to the Mass Customization development in a variety of products and services in the future.

6.2. Limitations and challenges

In this study, we encountered and summarized several limitations and challenges during the parametric eyeglasses design process.

6.2.1. Optimizable algorithm capacity

The parametric algorithm weaves various parameters into a network, where multiple values and variables can affect each other in a mutual way. For example, when the frame length and height change, the lens cavity shape will accordingly change based on the uniform ratio between length and height. However, uncertainties exist when fuzzy deformation happens due to such interactive effects. Taking the eyewear arms as an example, the arms start at the hinge points which connect to the frame's outer edges whereas the total arm breadth is mainly dependent on the head breadth. If the subject's front face breadth is significantly larger or smaller compared to the head width, it will result in a crooked arm shape from the temple to the ear. This being said, the current recruitment sample size with only the two subjects is yet sufficient to verify the parametric algorithm as a fully developed design tool. A more inclusive and diverse test study is required to further refine and improve the algorithm capacity.

6.2.2. Reliable evaluation process

Another challenge is to validate the method in a more reliable and objective way once an expanded sample size is recruited for the fit test evaluation. The fit and comfort are challenging to evaluate because they are largely depended on personal perceptions and opinions as well as partially affected by personal aesthetics. Our current planned evaluation process is to 3D print the eyewear prototypes for subjects, request the subjects to perform several simple tasks of daily movements, complete a self-report questionnaire about fit and comfort, and conduct an interview about the custom-fit eyewear experience. However, this process can cause bias due to random errors from different personal preferences or habits. Therefore, beyond the current design and evaluation strategy, more measurable and quantifiable interventions can be added to the overall study method. A potential solution is to collect measurable data of fit with sensor technologies. Sensor-based fit evaluations have been widely used in many studies [18,19]. For eyewear, embedding pressure sensors into the key skin-contact locations to detect pressure and temperature is a feasible way for further studies. This also requires modifying the eyewear structure and parametric algorithm to accommodate the potential locations for housing the sensor technologies.

6.2.3. Improvable prototyping and manufacturing

Beyond the parametric design and evaluation process, the prototyping quality also has an important impact on fit and comfort. Mass-produced eyeglasses are mostly made of fine-polished resinous material with silicone, rubber, and metal subassemblies and can offer softer and smoother skin contact. Our current study uses resin PLA (Polylactic acid) 3D print for quick prototyping and iterations, which can produce accurate structure and dimensions of the product. However, the plastic-like texture and coarse finishing quality might cause biases during the evaluation process due to its material and aesthetic imperfections. As PLA 3D print offers low-cost and efficient trials for validating the concept of this study, many high-resolution 3D printing services with polished-finishing material (e.g., SLS (Selective laser sintering) 3D print with Metal, Carbon Fiber or Resin) can provide optimized solutions for producing end-products [20].

Besides 3D printing, other innovative techniques, strategies, and manufacturing processes can support customization implementation. On the one hand, bringing a certain level of modularity in the parametric design system can largely reduce the complexity and costs of production [21]. On the other hand, the traditional manufacturing process such as molding and CNC (Computerized Numerical Control), can be applied in conjunction with the Mass Customization manufacturing processes [16]. One example from Montalto's research team experimented with a modularized thermoforming molding set that can reconfigure the curvature and shapes for eyewear front frames [22]. The parametric design method essentially “decomposes” the product into geometrical components to be customized, based on which we can further explore and apply the modularity to the frame design. By providing adjustability and assembly upon controls and constraints, the challenges of producing unitary and unique design can be compromised.

6.3. Future study

The results from the case study provided insightful findings on the potentials, limitations, and challenges of the parametric design method for wearable product designs.

An area for future study is to further test the method, refine the design workflow, and develope a more quantitative fit evaluation process. An important step in the future development is to conduct a fit test evaluation with a more reliable dataset with expaned sample size. With more subjects with a diversity of demographic backgrounds, we can improve the body-product relationship and parametric algorithm settings. This includes defining more accurate parameter values, correct constraints and tolerances among product dimensions, as well as enlarging the capacity of the parametric algorithm to accommodate a larger range of head-and-face shapes and sizes. In addition, for the purpose of gathering more objective fit valuation results, we suggest providing quantitative assessment approaches, possibly with the assistance of the sensor technology. A last but important factor that can affect the evaluation results is the prototyping quality. In the future study, we propose to update the 3D print prototyping with higher-resolution filament and post-fabrication finishing process to create prototypes that are closer in quality to what is commercially available.

To summarize, this study explores a newly developed parametric design method accompanied by 3D scan technology and anthropometric knowledge. The experiment case on custom-fit eyewear frames verifies the feasibility and potential of broader design opportunities for wearable products. We expect that this method can be adopted in a larger field of applications and motivate design development facing the new chapter of Mass Customization.

Author contribution statement

Yuanqing Tian: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Wrote the paper.

Roger Ball: Conceived and designed the experiments; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Data availability statement

No data was used for the research described in the article.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Biographies

Yuanqing Tian, Yuanqing Tian is a current Ph.D. candidate and design researcher at the School of Industrial Design, Georgia Institute of Technology. Working with Dr. Roger Ball in the Body Scan Lab, her doctoral research focuses on developing a systematic and methodological framework of parametric design for creating custom-fit wearable products. This research aim has been involved in many of her design and research projects of eyewear, bras, respirators, etc., with a wide knowledge and skillset including 3D scan technologies, anthropometric studies, and UI/UX design.

Dr. Roger Ball, Roger Ball has been crafting iconic sports products since 1983 for Burton Snowboards, Fisher Price, Brine Lacrosse, Bell Helmets and Nike. During his 25-year teaching career, he has led design studios in USA, Asia and the EU. As a Professor of Industrial Design at Georgia Tech Roger and his team in the Body Scan Lab develop design tools for human fit wearables using the latest body scanning and parametric design technologies. His award-winning 3D anthropometric study, SizeChina, created the first digital database of Chinese head and face shapes. As the founder of the Asian Ergonomic Lab at the Hong Kong Polytechnic University his team drove the development of ‘China-fit” products for global brands. Rogers research clients include Amazon, Google, Luxottica, Microsoft, 3 M, Cartier, Neurosky and cirque du soleil. Professor Ball holds an MFA from the Domus Academy in Milan and a PhD in Design Engineering from TUDeflt University in the Netherlands. He is a visiting Chair Professor of Industrial Design at Hunan University in Changsha China.

Appendix A. Supplementary data

The following are the Supplementary data to this article.