Approaches to the study of haptic sensing

Masking interferes with haptic texture perception from sequential exploratory movements

Haptic texture perception is based on sensory information sequentially gathered during several lateral movements ("strokes"). In this process, sensory information of earlier strokes must be preserved in a memory system. We investigated whether this system may be a haptic sensory memory. In the first experiment, participants performed three strokes across each of two textures in a frequency discrimination task. Between the strokes over the first texture, participants explored an intermediate area, which presented either a mask (high-energy tactile pattern) or minimal stimulation (low-energy smooth surface). Perceptual precision was significantly lower with the mask compared with a three-strokes control condition without an intermediate area, approaching performance in a one-stroke-control condition. In contrast, precision in the minimal stimulation condition was significantly better than in the one-stroke control condition and similar to the three-strokes control condition. In a second experiment, we varied the number of strokes across the first stimulus (one, three, five, or seven strokes) and either presented no masking or repeated masking after each stroke. Again, masking between the strokes decreased perceptual precision relative to the control conditions without masking. Precision effects of masking over different numbers of strokes were fit by a proven model on haptic serial integration (Lezkan & Drewing, Attention, Perception, & Psychophysics 80(1): 177-192, 2018b) that modeled masking by repeated disturbances in the ongoing integration. Taken together, results suggest that masking impedes the processes of haptic information preservation and integration. We conclude that a haptic sensory memory, which is comparable to iconic memory in vision, is used for integrating sequentially gathered sensory information.

The Minnesota Haptic Function Test

Haptic loss severely compromises the fine motor control of many daily manual tasks. Today, no widely accepted assessment protocols of haptic function are in clinical use. This is primarily due to the scarcity of fast, objective measures capable of characterizing mild to severe forms of haptic dysfunction with appropriate resolution. This study introduces a novel curvature-perception assessment system called the Minnesota Haptic Function Test™ that seeks to overcome the shortcomings of current clinical assessments.

Aims: The purpose of this study was threefold: (1) apply the test to a sample of young healthy adults to establish test-specific adult norms for haptic sensitivity and acuity; (2) establish the reliability of this instrument; (3) demonstrate clinical efficacy in a limited sample of cancer survivors who may exhibit haptic dysfunction due to chemotherapy-induced peripheral neuropathy.

Method: Participants manually explored two curved surfaces successively and made verbal judgments about their curvature. A Bayesian-based adaptive algorithm selected presented stimulus pairs based on a subject’s previous responses, which ensured fast convergence toward a threshold. Haptic sensitivity was assessed by obtaining detection thresholds in 26 adults (19–34 years). Haptic acuity was assessed by obtaining just-noticeable-difference thresholds in a second sample of 28 adults (19–25 years). Nine cancer survivors (18–25 years) with suspected peripheral neuropathy completed the acuity assessment. Test-retest reliability of the algorithm was calculated.

Results: First, the test yielded values that are consistent with those reported in the literature. Mean detection threshold for curvature of the healthy adults was 0.782 (SD ± 0.320 m⁻¹). The corresponding mean discrimination threshold was 1.030 (SD ± 0.462 m⁻¹). Second, test-retest reliability of the algorithm was assessed in a simulation, yielding an average correlation between repeated simulated thresholds of r = 0.93. Third, the test documented that 86% of the cancer survivors had acuity thresholds above the 75th percentile of the normative cohort, and 29% had thresholds above the normal range, indicating that the instrument can detect and differentiate between unaffected perception, and mild or more severe forms of haptic loss.

Conclusion: We here provide evidence that this new method to assess haptic perception of curvature is valid, reliable, and clinically practicable.

Interdependences between finger movement direction and haptic perception of oriented textures

Although the natural haptic perception of textures includes active finger movements, it is unclear how closely perception and movements are linked. Here we investigated this question using oriented textures. Textures that are composed of periodically repeating grooves have a clear orientation defined by the grooves. The direction of finger movement relative to texture orientation determines the availability of temporal cues to the spatial period of the texture. These cues are absent during movements directed in line with texture orientation, whereas movements orthogonal to texture orientation maximize the temporal frequency of stimulation. This may optimize temporal cues. In Experiment 1 we tested whether texture perception gets more precise the more orthogonal the movement direction is to the texture. We systematically varied the movement direction within a 2IFC spatial period discrimination task. As expected, perception was more precise (lower discrimination thresholds) when finger movements were directed closer towards the texture orthogonal as compared to in parallel to the texture. In Experiment 2 we investigated whether people adjust movement directions to the texture orthogonal in free exploration. We recorded movement directions during free exploration of standard and comparison gratings. The standard gratings were clearly oriented. The comparison gratings did not have a clear orientation defined by grooves. Participants adjusted movement directions to the texture orthogonal only for clearly oriented textures (standards). The adjustment to texture orthogonal was present in the final movement but not in the first movement. This suggests that movement adjustment is based on sensory signals for texture orientation that were gathered over the course of exploration. In Experiment 3 we assessed whether the perception of texture orientation and movement adjustments are based on shared sensory signals. We determined perceptual thresholds for orientation discrimination and computed 'movometric' thresholds from the stroke-by-stroke adjustment of movement direction. Perception and movements were influenced by a common factor, the spatial period, suggesting that the same sensory signals for texture orientation contribute to both. We conclude that people optimize texture perception by adjusting their movements in directions that maximize temporal cue frequency. Adjustments are performed on the basis of sensory signals that are also used for perception.

Shape Localization and Recognition Using a Magnetorheological-Fluid Haptic Display

Smart materials such as magnetorheological fluids (MRF) offer an interesting technology for use in haptic displays as changes in the magnetic field are rapid, reversible, and controllable. These interfaces have been evaluated in a number of medical and surgical simulators where they can provide cues regarding the viscoelastic properties of tissues. The objective of the present set of experiments was first to determine whether a shape embedded in the MRF could be precisely localized and second whether 10 shapes rendered in a MRF haptic display could be accurately identified. It was also of interest to determine how the information transfer associated with this type of haptic display compares to that achieved using other haptic channels of communication. The overall performance of participants at identifying the shapes rendered in the MRF was good with a mean score of 73 percent correct and an Information Transfer (IT) of 2.2 bits. Participants could also localize a rigid object in the display accurately. These findings indicate that this technology has potential for use in training manual palpation skills and in exploring haptic shape perception in dynamic environments.

Processing of haptic texture information over sequential exploration movements

Where textures are defined by repetitive small spatial structures, exploration covering a greater extent will lead to signal repetition. We investigated how sensory estimates derived from these signals are integrated. In Experiment 1, participants stroked with the index finger one to eight times across two virtual gratings. Half of the participants discriminated according to ridge amplitude, the other half according to ridge spatial period. In both tasks, just noticeable differences (JNDs) decreased with an increasing number of strokes. Those gains from additional exploration were more than three times smaller than predicted for optimal observers who have access to equally reliable, and therefore equally weighted, estimates for the entire exploration. We assume that the sequential nature of the exploration leads to memory decay of sensory estimates. Thus, participants compare an overall estimate of the first stimulus, which is affected by memory decay, to stroke-specific estimates during the exploration of the second stimulus. This was tested in Experiments 2 and 3. The spatial period of one stroke across either the first or second of two sequentially presented gratings was slightly discrepant from periods in all other strokes. This allowed calculating weights of stroke-specific estimates in the overall percept. As predicted, weights were approximately equal for all strokes in the first stimulus, while weights decreased during the exploration of the second stimulus. A quantitative Kalman filter model of our assumptions was consistent with the data. Hence, our results support an optimal integration model for sequential information given that memory decay affects comparison processes.

Differences in curvature between constrained and unconstrained goal-directed movements to haptic targets

Trajectories of goal-directed movements are less curved for movements over a surface (constrained) than for movements in empty space (unconstrained). To study whether this difference arises from feeling the surface slip across the skin or having to control the movements in a third dimension, we manipulated the available tactile information and the compliance of the surface. Participants were instructed to make straight movements towards haptic targets in the mid-sagittal plane. We found that constrained movements were less curved than unconstrained movements. The reduction of curvature was also visible with strongly reduced tactile information and for very compliant surfaces, so feeling the surface slip across the skin and having to control the movements in the third dimension are not critical. The reduced curvature when moving over a surface might arise from the extra information that the surface gives about the third dimension or from the extra information about the direction of the movement provided by the additional force needed to overcome friction.

Bimanual proprioception: are two hands better than one?

Information about the position of an object that is held in both hands, such as a golf club or a tennis racquet, is transmitted to the human central nervous system from peripheral sensors in both left and right arms. How does the brain combine these two sources of information? Using a robot to move participant's passive limbs, we performed psychophysical estimates of proprioceptive function for each limb independently and again when subjects grasped the robot handle with both arms. We compared empirical estimates of bimanual proprioception to several models from the sensory integration literature: some that propose a combination of signals from the left and right arms (such as a Bayesian maximum-likelihood estimate), and some that propose using unimanual signals alone. Our results are consistent with the hypothesis that the nervous system both has knowledge of and uses the limb with the best proprioceptive acuity for bimanual proprioception. Surprisingly, a Bayesian model that postulates optimal combination of sensory signals could not predict empirically observed bimanual acuity. These findings suggest that while the central nervous system seems to have information about the relative sensory acuity of each limb, it uses this information in a rather rudimentary fashion, essentially ignoring information from the less reliable limb.

Predictive mechanisms in the control of contour following

In haptic exploration, when running a fingertip along a surface, the control system may attempt to anticipate upcoming changes in curvature in order to maintain a consistent level of contact force. Such predictive mechanisms are well known in the visual system, but have yet to be studied in the somatosensory system. Thus, the present experiment was designed to reveal human capabilities for different types of haptic prediction. A robot arm with a large 3D workspace was attached to the index fingertip and was programmed to produce virtual surfaces with curvatures that varied within and across trials. With eyes closed, subjects moved the fingertip around elliptical hoops with flattened regions or Limaçon shapes, where the curvature varied continuously. Subjects anticipated the corner of the flattened region rather poorly, but for the Limaçon shapes, they varied finger speed with upcoming curvature according to the two-thirds power law. Furthermore, although the Limaçon shapes were randomly presented in various 3D orientations, modulation of contact force also indicated good anticipation of upcoming changes in curvature. The results demonstrate that it is difficult to haptically anticipate the spatial location of an abrupt change in curvature, but smooth changes in curvature may be facilitated by anticipatory predictions.

Methodology for evaluating gloves in relation to the effects on hand performance capabilities: a literature review

The present study was conducted to review the literature on the methods that have been considered appropriate for evaluation of the effects of gloves on different aspects of hand performance, to make recommendations for the testing and assessment of gloves, and to identify where further research is needed to improve the evaluation protocols. Eighty-five papers meeting the criteria for inclusion were reviewed. Many studies show that gloves may have negative effects on manual dexterity, tactile sensitivity, handgrip strength, muscle activity and fatigue and comfort, while further research is needed to determine glove effects on pinch strength, forearm torque strength and range of finger and wrist movements. The review also highlights several methodological issues (including consideration of both task type and duration of glove use by workers, guidance on the selection and allocation of suitable glove(s) for particular tasks/jobs, and glove design features) that need to be considered in future research. Practitioner Summary: The relevant literature on the effects of protective gloves on different aspects of hand performance was reviewed to make recommendations for the testing and assessment of gloves, and to improve evaluation protocols. The review highlights research areas and methodological issues that need to be considered in future research.

The role of visual experience for the neural basis of spatial cognition

Blindness often results in the adaptive neural reorganization of the remaining modalities, producing sharper auditory and haptic behavioral performance. Yet, non-visual modalities might not be able to fully compensate for the lack of visual experience as in the case of congenital blindness. For example, developmental visual experience seems to be necessary for the maturation of multisensory neurons for spatial tasks. Additionally, the ability of vision to convey information in parallel might be taken into account as the main attribute that cannot be fully compensated by the spared modalities. Therefore, the lack of visual experience might impair all spatial tasks that require the integration of inputs from different modalities, such as having to represent a set of objects on the basis of the spatial relationships among the objects, rather than the spatial relationship that each object has with oneself. Here we integrate behavioral and neural evidence to conclude that visual experience is necessary for the neural development of normal spatial cognition.

Two hands, one perception: how bimanual haptic information is combined by the brain

Humans routinely use both of their hands to gather information about shape and texture of objects. Yet, the mechanisms of how the brain combines haptic information from the two hands to achieve a unified percept are unclear. This study systematically measured the haptic precision of humans exploring a virtual curved object contour with one or both hands to understand if the brain integrates haptic information from the two hemispheres. Bayesian perception theory predicts that redundant information from both hands should improve haptic estimates. Thus exploring an object with two hands should yield haptic precision that is superior to unimanual exploration. A bimanual robotic manipulandum passively moved the hands of 20 blindfolded, right-handed adult participants along virtual curved contours. Subjects indicated which contour was more “curved” (forced choice) between two stimuli of different curvature. Contours were explored uni- or bimanually at two orientations (toward or away from the body midline). Respective psychophysical discrimination thresholds were computed. First, subjects showed a tendency for one hand to be more sensitive than the other with most of the subjects exhibiting a left-hand bias. Second, bimanual thresholds were mostly within the range of the corresponding unimanual thresholds and were not predicted by a maximum-likelihood estimation (MLE) model. Third, bimanual curvature perception tended to be biased toward the motorically dominant hand, not toward the haptically more sensitive left hand. Two-handed exploration did not necessarily improve haptic sensitivity. We found no evidence that haptic information from both hands is integrated using a MLE mechanism. Rather, results are indicative of a process of “sensory selection”, where information from the dominant right hand is used, although the left, nondominant hand may yield more precise haptic estimates.

Multiple Factors Underlying Haptic Perception of Length and Orientation

Information about the shape and spatial orientation of an object can be gathered during exploratory hand and arm movements, and then must be synthesized into a unified percept. During the robotically guided exploration of virtual polygons or triangles, the perception of the lengths of two adjoining segments is not always geometrically consistent with the perception of the internal angles between these segments. The present study further characterized this established inconsistency, and also found that subjects' internal angle judgments were influenced by the spatial orientations of the segments, especially the segment that was explored last in the sequence. Internal angle judgments were also biased by the subjects' own active forces, applied in the direction perpendicular to the programmed handle motion. For the last segment, but not for the earlier segments, subjects produced more outward force when they reported larger angles and more inward force when they reported smaller angles. Thus, the haptic synthesis of object shape is influenced by multiple geometric, spatial, and self-produced factors.

The effects of secondary task interference on shape reproduction

The influence of a secondary task on speeded responses, and its effect on the outcome of more complex tasks has been studied in detail. However, the consequence of task interference on specific movement parameters other than speed and accuracy has been largely ignored. The current study examines how performing a secondary task impacts the drawing of an unseen shape. Without vision of the hand, 15 subjects traced a shape on a graphics tablet. The shape and cursor were projected onto a screen. The shape disappeared and the subject attempted to draw three consecutive identical shapes. In the visual single-task condition, hand positions were represented by a cursor, but the resultant drawings could not be seen; in another, there was no visual feedback. In four remaining conditions, the 15 subjects drew the previously seen shapes without visual feedback while performing a secondary task of reporting the orientation of an arrow which appeared on the screen either in random or periodic timing. Subjects indicated the direction of the arrow either verbally or manually. Shapes were analyzed for scale, error of the corner angles as compared with 90 degrees, and drift, compared to the reference shape and across conditions. In dual-task conditions, performance of the primary, shape-drawing task deteriorated with respect to location and orientation, but not with respect to the pattern and proportion aspects of the shape. Vision was important for controlling position of the drawing, and also for controlling the shape and proportion of the drawing suggesting separate mechanisms for the location of a drawing and its shape and proportion. Furthermore, we propose that internal representations are more important than proprioception in the shape aspect of drawing well-known figures.

Sensorimotor control of contact force

Interacting with objects in the environment introduces several new challenges for motor control: the potential for instability, external constraints on possible motions and novel dynamics. Grasping and manipulating objects provide the most elaborate examples of such motor tasks. We review each of these topics and suggest that when sensory feedback is reliable, it is used to adapt the motion to the requirements imposed by the object. When sensory feedback is unreliable, subjects adapt the stiffness of muscles and joints to the task's requirements. One of the simplifications introduced in the control of such movements is a reduction in the effective number of degrees of freedom (sensorimotor axes and muscle synergies) and recent findings and methodological considerations relevant to this topic are discussed.

Haptic perception of object curvature in Parkinson's disease

Background

The haptic perception of the curvature of an object is essential for adequate object manipulation and critical for our guidance of actions. This study investigated how the ability to perceive the curvature of an object is altered by Parkinson's disease (PD).

Methodology/Principal Findings

Eight healthy subjects and 11 patients with mild to moderate PD had to judge, without vision, the curvature of a virtual “box” created by a robotic manipulandum. Their hands were either moved passively along a defined curved path or they actively explored the curved curvature of a virtual wall. The curvature was either concave or convex (bulging to the left or right) and was judged in two locations of the hand workspace–a left workspace location, where the curved hand path was associated with curved shoulder and elbow joint paths, and a right workspace location in which these joint paths were nearly linear. After exploring the curvature of the virtual object, subjects had to judge whether the curvature was concave or convex. Based on these data, thresholds for curvature sensitivity were established. The main findings of the study are: First, 9 out 11 PD patients (82%) showed elevated thresholds for detecting convex curvatures in at least one test condition. The respective median threshold for the PD group was increased by 343% when compared to the control group. Second, when distal hand paths became less associated with proximal joint paths (right workspace), haptic acuity was reduced substantially in both groups. Third, sensitivity to hand trajectory curvature was not improved during active exploration in either group.

Conclusion/Significance

Our data demonstrate that PD is associated with a decreased acuity of the haptic sense, which may occur already at an early stage of the disease.

Differential effects of non-informative vision and visual interference on haptic spatial processing

The primary purpose of this study was to examine the effects of non-informative vision and visual interference upon haptic spatial processing, which supposedly derives from an interaction between an allocentric and egocentric reference frame. To this end, a haptic parallelity task served as baseline to determine the participant-dependent biasing influence of the egocentric reference frame. As expected, large systematic participant-dependent deviations from veridicality were observed. In the second experiment we probed the effect of non-informative vision on the egocentric bias. Moreover, orienting mechanisms (gazing directions) were studied with respect to the presentation of haptic information in a specific hemispace. Non-informative vision proved to have a beneficial effect on haptic spatial processing. No effect of gazing direction or hemispace was observed. In the third experiment we investigated the effect of simultaneously presented interfering visual information on the haptic bias. Interfering visual information parametrically influenced haptic performance. The interplay of reference frames that subserves haptic spatial processing was found to be related to both the effects of non-informative vision and visual interference. These results suggest that spatial representations are influenced by direct cross-modal interactions; inter-participant differences in the haptic modality resulted in differential effects of the visual modality.

The haptic perception of spatial orientations

This review examines the isotropy of the perception of spatial orientations in the haptic system. It shows the existence of an oblique effect (i.e., a better perception of vertical and horizontal orientations than oblique orientations) in a spatial plane intrinsic to the haptic system, determined by the gravitational cues and the cognitive resources and defined in a subjective frame of reference. Similar results are observed from infancy to adulthood. In 3D space, the haptic processing of orientations is also anisotropic and seems to use both egocentric and allocentric cues. Taken together, these results revealed that the haptic oblique effect occurs when the sensory motor traces associated with exploratory movement are represented more abstractly at a cognitive level.

Assessing the skills of surgical residents using simulation

Much is still to be learned about the assessment of simulation-based surgical skills training. However, assessing surgery skills through simulation is a new horizon in medical education. Providing a safe environment for surgical residents to assess their performance rigorously without placing patients in jeopardy is valuable. Using simulators (both warm and cold) as a means to assess trainees has been established. However, also problems concerning the validity and reliability of such simulation-based assessment tools exist, particularly in surgery, that may need to be investigated even more to decide whether to use them as a tool for assessing the performance of surgical residents.

Shape distortion produced by isolated mismatch between vision and proprioception

To investigate the nature of the visuomotor transformation, previous studies have used pointing tasks and examined how adaptation to a spatially localized mismatch between vision and proprioception generalizes across the workspace. Whereas some studies found extensive spatial generalization of single-point remapping, consistent with the hypothesis of a global realignment of visual and proprioceptive spaces, other studies reported limited transfer associated with variations in initial limb posture. Here, we investigated the effects of spatially localized remapping in the context of a visuomanual tracking task. Subjects tracked a visual target tracing a simple two-dimensional geometrical form without visual feedback except at a single point, where the visual display of the hand was shifted relative to its actual position. After adaptation, hand paths exhibited distortions relative to the visual templates that were inconsistent with the idea of a global realignment of visual and proprioceptive spaces. Results of a visuoproprioceptive matching task showed that these distortions were not limited to active movements but also affected perception of passive limb movements.

Factors influencing the radial-tangential illusion in haptic perception

According to the radial-tangential illusion, in the horizontal plane, arm movements executed in directions radial to the trunk are sensed to be longer than movements of the same length in the orthogonal direction. It has been suggested that the illusion arises from the fact that radially directed movements are executed more slowly and require more effort. These suggestions were tested in a series of experiments, using a robotically controlled manipulandum. In all of the experiments subjects grasped the handle of the manipulandum, in some cases exploring the virtual boundary of a rectangle, while in others being guided along a rectangular contour by the robot. In a two-alternative forced choice design, subjects reported whether the rectangle was wide or narrow. In a control experiment, subjects manifested the radial-tangential illusion. Contrary to the hypothesis, the magnitude of this illusion was not altered when a resistive force was added in the tangential direction or when the ratio of movement times in the tangential and radial directions was changed. However, when the contour was explored in the counterclockwise direction, the illusion was much smaller than when it was explored in the clockwise direction. A second series of experiments, in which subjects only explored two sides (i.e., an L-shape), demonstrated that this effect arose from distortions induced by the serial ordering of the exploratory movements. The illusion was much smaller when the radial segment was explored first. We suggest that this distortion arises from the serial nature of haptic exploration, in which the length of the initial segment decreases as it is stored in working memory for subsequent comparison.

Learning to perform a new movement with robotic assistance: comparison of haptic guidance and visual demonstration

BACKGROUND

Mechanical guidance with a robotic device is a candidate technique for teaching people desired movement patterns during motor rehabilitation, surgery, and sports training, but it is unclear how effective this approach is as compared to visual demonstration alone. Further, little is known about motor learning and retention involved with either robot-mediated mechanical guidance or visual demonstration alone.

METHODS

Healthy subjects (n = 20) attempted to reproduce a novel three-dimensional path after practicing it with mechanical guidance from a robot. Subjects viewed their arm as the robot guided it, so this "haptic guidance" training condition provided both somatosensory and visual input. Learning was compared to reproducing the movement following only visual observation of the robot moving along the path, with the hand in the lap (the "visual demonstration" training condition). Retention was assessed periodically by instructing the subjects to reproduce the path without robotic demonstration.

RESULTS

Subjects improved in ability to reproduce the path following practice in the haptic guidance or visual demonstration training conditions, as evidenced by a 30-40% decrease in spatial error across 126 movement attempts in each condition. Performance gains were not significantly different between the two techniques, but there was a nearly significant trend for the visual demonstration condition to be better than the haptic guidance condition (p = 0.09). The 95% confidence interval of the mean difference between the techniques was at most 25% of the absolute error in the last cycle. When asked to reproduce the path repeatedly following either training condition, the subjects' performance degraded significantly over the course of a few trials. The tracing errors were not random, but instead were consistent with a systematic evolution toward another path, as if being drawn to an "attractor path".

CONCLUSION

These results indicate that both forms of robotic demonstration can improve short-term performance of a novel desired path. The availability of both haptic and visual input during the haptic guidance condition did not significantly improve performance compared to visual input alone in the visual demonstration condition. Further, the motor system is inclined to repeat its previous mistakes following just a few movements without robotic demonstration, but these systematic errors can be reduced with periodic training.

Haptic feature extraction

This study examined the process by which the shape of a haptically explored object is synthesized from the geometric characteristics of simpler constituent elements, such as arcs and ellipses. Subjects traced the outlines of virtual objects by means of whole arm movements. Each object consisted of the union of a large central ellipse and two smaller circles, extending upward and outward from the top left and right sides of the base. The sizes of the two circles and the eccentricity of the elliptical base were varied. After exploring the object's contour in the absence of vision, subjects reproduced the sensed shape by means of freehand drawing. Speed and force were modulated during the exploratory phase in a manner that suggested that subjects reacted to rather than predicted changes in curvature. Also, subjects typically devoted more time to exploring the part of the contour encompassing the two smaller circles. During drawing, individual features of the explored shape were reproduced with varying degrees of fidelity. Aspects related to the size and location of the smaller circles were reproduced better than was the eccentricity of the ellipse forming the base. Since subjects spent proportionally less time exploring the base, these results suggest that subjects selectively focused attention to regions of high spatial contrast and that the exploratory strategy introduced distortions in the haptically sensed shapes.