Patent Application
20090122008
The present invention relates to methods and systems for optically measuring and locating points on two-dimensional surfaces or in three-dimensional volumes.
Methods and systems for capturing coordinates of points-or locations-of real-world surfaces for input into computer-aided design (CAD) software are in widespread use. The points may be on a two-dimensional (2D) surface or on the exterior of a three-dimensional (3D) object. The process of inputting coordinates of points of a 2D medium or a 3D object into a computer memory is commonly called digitizing. For example, a digitizing tablet may be used to input XY coordinates of sampled points on a 2D image—such as a photograph, blueprint, or pencil-sketched drawing—in order to build a CAD or other computer graphics representation of the salient geometric features of the image.
Similarly, a “cloud of points” may be sampled from the 3D surface of a physical object to build a data representation (or model) of the geometry of the physical object in a computer memory. Each sampled point may be represented by an XYZ coordinate triple. In a more sophisticated representation, the cloud of points may be converted into vertices of abutting planar polygonal patches which approximate the surface of the object. In a more sophisticated representation, the cloud of points may be converted into abutting curved polygonal patches. Each patch, whether planar or curved, may be defined by a mathematical bivariate polynomial or rational function—such as in the NURBS surfaces commonly used in computer graphics. In special cases, 3D data entry may rely on real-world measurements where the generic geometric shape (e.g., circle, sphere, cube, cylinder, etc.) of a real-world object is known, but the dimensions of the shape must be determined by physically measuring the coordinates of one or more points to quantify the shape.
Numerous approaches exist for measuring real-world surface points. For planar media, various 2D digitizing tablets are commercially available which are commonly used in computer-aided drafting and design. The two most common input devices are a hand-held pen-like stylus with a pointing tip, and a manually moveable cursor-also called a puck. The movable cursor may have a reticle scribed into a transparent plate which can be moved over the surface of the tablet or a planar medium on the tablet. A common form of a reticle is pair of crosshairs. The reticle may include an indicator, such as an arrow tip or the intersection of the crosshairs, which indicates the particular surface point to be measured by the moveable cursor.
A probe may be used to input of points on the surface of a 3D object. Such a probe may have a pointer, tip, or other indicator for indicating an individual location on the object. The indicator may be a sharp conical pointer, a spherical tip of known radius, a grooved tip for tracing edges, or a roller of known radius.
Generally, the location of the indicator on the probe, cursor, or puck is measured in two or three dimensions by a coordinate measuring system, referred to herein as a tracker. The tracker may not track the indicator directly, but instead track sensible markers spaced apart from the indicator. In many cases, placing a sensible marker exactly at the location of the indicator would be problematic, because the size or the opacity of the marker may obscure the indicator from view. This problem may be avoided by tracking two or more markers positioned with a known geometrical relationship with respect to the indicator, so the location of the indicator may be computed from the locations of the markers.
The various embodiments provide methods and systems for measuring a 2D or 3D location in a coordinate system using only one marker on a probe. The probe contains an indicator to designate the location of a specific point on a 2D surface or in a 3D volume for the measurement of the location. A single trackable marker on the probe effectively has the same location as the indicator without blocking a user's view of the indicator. An embodiment measures the location of the marker with a tracker, which may report the location as 2D or 3D coordinates in a coordinate system.
An embodiment is configured so that the indicator lies at a known offset and at a constrained direction from the marker. An embodiment for a planar or 2D application positions the marker and the indicator on the same line normal (perpendicular) to the surface. An embodiment for 3D applications uses the known offset and direction of the marker to compute the location of the indicator in the plane of the medium.
Another embodiment virtually collocates a probe's marker and indicator by using a mirror—or an equivalent reflecting surface for a sonic marker. In this embodiment, the indicator and the marker lie on opposite sides of the mirror's reflecting surface at equal distances from the reflecting surface and on a line perpendicular to the reflecting surface. This configuration causes the location of a virtual image of the marker to coincide with the location of the indicator. In alternative embodiments, the mirror may be planar or non-planar.
A portion of the probe including the marker and the mirror may be hinged or moveable as long as the image of the marker continues to coincide with the indicator.
The accompanying drawings, which are incorporated herein and constitute part of this specification, illustrate presently preferred embodiments of the invention, and, together with the general description given above and the detailed description given below, serve to explain features of the invention.
Various embodiments of the present invention will be described in detail with reference to the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts.
Generally, the location of the indicator of a probe of a 2D digitizing tablet or a 3D tracking system is measured relative to a coordinate system. The coordinate system typically may be a standard Cartesian (rectangular) coordinate system, possibly defined by the user with respect to the medium or object being digitized. The location of the indicator of a probe relative to the coordinate system is typically determined by a marker coordinate measurement system, referred to herein as a tracker. For digitizing points on a plane, the tracker typically reports the location of the indicator of a 2D probe as numerical X and Y coordinates. An example of a 2D tracker is a planar digitizing tablet, which may be constructed with marker location sensing wires buried in the digitizing tablet. A family of such tablets is available from Wacom Technology Corp. (Vancouver, Wash.). For digitizing points in a 3D volume, the tracker typically reports the location of the indicator of a 3D probe as X, Y, and Z coordinates. An example of a handheld, optically tracked probe and its 3D tracker are the FlashPoint and 3D Creator products sold by Boulder Innovation Group, Inc. (Boulder, Colo.).
Both 2D and 3D probes generally incorporate at least one localized, trackable, physically sensible marker. Each sensible physical marker is a feature which defines a reference point on the probe. A marker may be a point-like light source, a light detector, a retro-reflector, a high-contrast target pattern, a sound emitter, a magnetic coil, or another sensible physical feature. The location of each marker may be measured essentially continuously by the tracker. For example, each marker may have an optical characteristic, such as an illuminated spot having a centroid, the location of which is precisely measured by an optical tracker. Optical trackers may measure the marker location using visible, infrared or ultraviolet spectra. Other types of trackers measure the location of a marker on a 2D surface or in a 3D volume using ultrasound or magnetic fields instead of light.
A reticle of a cursor and the pointing tip of a probe both are referred to herein as an indicator. The stylus, cursor, or puck for 2D digitizing and the probe used for 2D or 3D digitizing are referred to as a probe. Each probe includes an indicator that indicates the specific, single point on which the indicator lies or which the indicator contacts at a given moment.
It has often been impractical to locate a single sensible marker at exactly the same location on the probe as the indicator. One reason is that markers, being generally opaque, would block a user's view of the indicator if collocated with the indicator. That is, the indicator effectively would be inside and at the very center of the marker. Thus, the marker make it difficult for the user to position the indicator on the point to be measured (i.e., digitized). Aside from visibility problems, the physical volume of the marker would prevent the user from touching the indicator directly to the point to be digitized. For example, some optical trackers use a retro-reflective one-centimeter ball as a marker. That size marker would completely envelop and optically block the indicator if the indicator and marker were positioned concentrically on the probe. To resolve this problem, many probes include markers located some distance from the indicator to allow a user to visually place the indicator of the probe at a desired point for measurement. A tracker can measure the location of the marker and then compute the location of the indicator given the known offset and direction.
Many trackers only measure the location of a marker and not its orientation, especially when the marker is omni-directional, such as a single light-emitting diode (LED) or a retro-reflective ball. Consequently, a tracker cannot determine the location of the indicator based on the location of an omni-directional marker since it cannot determine the rotational orientation of the probe (and thus the offset direction of the marker with respect to the indicator). Therefore, a probe employing such markers generally requires at least two spaced-apart markers for 2D measurements and at least three spaced-apart markers for 3D measurements. Using the known relationship of the markers to the indicator and from the measured coordinates of the multiple markers, the coordinates of the indicator may be computed using well-known techniques of analytic geometry.
For example, there may be at least two markers at known distances from the indicator of the probe. Then, a tracker may compute the spatial coordinates of the indicator given the measured coordinates of the two markers. More generally, there may be three or more markers in known geometric relationships to the indicator. Techniques for computing the coordinates of the indicator from the measured coordinates of at least three markers are well known to persons of ordinary skill in the art of 2D or 3D digitizing. Commercial 2D digitizing tablets and 3D trackers and their probes regularly employ multiple markers on a probe for computing the location coordinates of the indicator on the probe.
Nevertheless, it can be advantageous to use only one marker on a probe. For example, some trackers do not measure the location coordinates of multiple markers at exactly the same moment. With such trackers, any motion of the probe between measurements can introduce error into the computation of the indicator location. Using only one marker on the probe with the marker collocated with the indicator can avoid such errors.
Alternatively, a reference frame 49 with its own sensible markers may be attached to the surface 12 and measured by the tracker 20 to register the coordinate system 19 of the tracker 20 with respect to the markers of the reference frame 49. Thereafter, as long as the reference frame 49 remains fixed, the coordinate system of the tracker 20 remains fixed with respect to the reference frame 49, and therefore fixed with respect to the surface 12. This remains true even when the tracker 20 is moved with respect to the surface 12. To register the tracker 20,
In use, the tracker 20 records the coordinates of one or more points of the surface 12 and communicates this information via a data cable 40 to the computer 50 for storage. Recording may conditionally take place when the user presses a button (41 in
The tracker 20 illustrated in
In an embodiment, the indicator 31 is scribed on the bottom of the transparent plate 35 so there can be no angular disparity between the location of the intersection of the indicator 31 and the point directly under the indicator 31. In this embodiment, the transparent plate 35 may be glass or plastic. In an alternative embodiment, the base plate 35 may be a thin slab of optical fiber image conduit, which optically raises the image of the surface 12 to the top of the base plate 35, so the indicator 31 may be scribed on the top of the base plate 35. In this embodiment, the optical fiber image conduit prevents any refractive shift (disparity) between the image of the surface 12 under the base plate 35 and the indicator 31.
During use of the probe 30, the base plate 35 and the indicator 31 are in contact with a surface 12 to be measured. The marker 32 is at a known offset from the indicator 31 and on the line from the indicator 31 perpendicular to the plane of the base plate 35. The marker 32 is offset from (e.g., positioned above) the indicator 31 in order not block the line-of-sight between the indicator 31 and a user. The offset enables the user 1 to place the indicator 31 of the probe 30 at the clearly visible location on the surface 12. The tracker 20 can determine the XY coordinates of the indicator 31 by measuring the coordinates of the marker 32 and by compensating for the known offset in the perpendicular direction of the marker with respect to the indicator 31.
The probe 30, shown as a puck in
The button 41 on the probe 30 may be pressed to control when XY coordinate measurements are made. Any well known switch circuit (not shown separately) may be mechanically coupled to the button 41, so that when a user pressing the button, an electrical signal (e.g., closing a circuit) is generated. In an embodiment, button 41 may be coupled to digital circuits to generate a digital signal in response to a user pressing the button. The button and associated switch circuitry are connected to communication circuitry so that the signal can be transmitted to the computer, such as by means of the data cable 40. In a simple embodiment, the communication circuitry is a simple conductor so that when the button is pressed, closing the switch circuitry, electrical energy is communicated through the conductor through the data cable 40 to the computer. In another embodiment, the communication circuitry is a digital communication bus configured to convey a digital signal from the switch circuitry to the data cable 40. In a further embodiment in which data is transmitted wirelessly instead of by means of a data cable 40, the communication circuitry includes a wireless data link transceiver as are well known in the art that is configured to receive a digital signal from the switch circuitry and communicate the information in the signal to the computer wirelessly. In use, when the probe 30 is centered on a particular point, a user presses the button 41 which in conjunction with associated switch and communication circuitry sends a signal to the computer indicating that a location measurement of the marker 32 should be taken.
The probe 30 may include a status light 44, such as an LED, or an audio transducer (not shown) to inform the user of success or failure of a particular coordinate measurement. To provide this functionality, the computer 50 may activate status light 44 by sending signals via the data cable 40. For example, the computer 50 may cause the status light 44 to flash to inform the user of a problem, such as blocked line-of-sight between the marker 32 and the tracker 20. The cable 40 may also provide power to the marker 32. The data cable 40 may be electrical or optical, and may be unidirectional or bidirectional.
In an alternative embodiment, communication between the probe and the computer 50 may be by way of a wireless data link (not shown as it is invisible). Such a wireless link may transmit and/or receive radio waves, infrared, sound, some other wireless medium, or a combination thereof to communicate information to and from the computer 50. The probe 30 may include a self-contained energy source, such as a battery (not shown) for powering the status light 44, marker 32 (if necessary) and data communication circuitry.
The marker 32 may be any of a variety of sensible marker. The marker 32 may be an active, point-like source of light, such as a light-emitting diode (LED), which may flash or emit light continuously. An LED may emit an infrared or visible wavelength. The marker 32 may be a small retro-reflective spot or ball, in which case there may be one or more sources of light on or near the tracker 20 to illuminate the marker 32. The marker 32 may be a passive, distinctively-colored or high-contrast shape or pattern, lit only by ambient light. An example of such a passive pattern is the checkered pattern tracked by the Micron Tracker of Claron Technologies (Toronto, Ontario, Canada). For an ultrasonic tracker 20, the marker 32 may be a piezoelectric crystal or a spark gap which emit sounds. For a magnetic tracker 20, the marker 32 may be a set of three tiny orthogonal induction coils.
As illustrated in
The embodiment illustrated in
To prevent the tracker 20 from seeing both the reflected virtual image of the marker 32 and the marker 32 itself, there may need to be one or more appropriately-placed opaque baffles or opaque portions of the housing 34. The top of the probe 30 housing 34 may be opaque, serving as such a baffle and obstructing the direct line of sight between the tracker 20 and the marker 32. The marker 32 may be mounted on the bottom side of the baffle or housing 34. The tracker 20 may include a light source 47 for illuminating the marker 32 via the mirror 33, enabling the use of a retro-reflective marker 32.
Another embodiment of a probe 30 is illustrated in
The embodiment illustrated in
Another embodiment is illustrated in
Paths of light emanating from a marker 32 in the direction of a tracker 20 are illustrated in
It should be noted that a similar probe configuration can be provided for an ultrasonic tracker, in which the equivalent of the mirror 33 may be a hard, sound-reflecting surface, and the sonic equivalent of an optical baffle may be a soft, deeply textured surface such as foam. Like light, sound from an ultrasound marker will be reflected off the sound-reflecting surface to create a virtual sonic source.
Some optical 3D trackers 20 may experience problems in circumstances where the line-of-sight to a marker is partially blocked by an intervening object. In such situations the optical tracker 20 may incorrectly measure the location of the marker. For example, if the marker is an LED or a retro-reflective ball, there may be an error in the measured coordinates because the centroid of the portion visible to the tracker 20 is offset from the actual center of the marker. For a one-centimeter retro-reflective ball, the positional error may be more than a millimeter. This problem may also occur with the probe embodiments described herein, such as, for example, when the user's hand partially blocks the line-of-sight from one of the cameras 21a-21c of the tracker 20 to the virtual image of the marker 32. However, conventional trackers 20 may not be able to detect this circumstance and warn the user.
For the probes described herein, there is an addition problematic circumstance in which the virtual image of the marker 32 can be partially blocked. The probe may be oriented so that the virtual image of the marker 32, as observed by a camera 21a-21c of the tracker 20, is reflected off the edge of the mirror 33. In such circumstances the impact on positional accuracy may be the same as when an intervening object partially blocks the line-of-sight to a marker 32.
An embodiment of a tracker 20 includes provisions to detect a partially blocked line-of-sight to a marker 32 or to the virtual image of a marker 32. Specifically, photodetectors 27 (which may be photodiodes) may be included on the tracker 20 for use with markers that are active LEDs or retro-reflective balls.
For example, if a marker 32 is partially blocked, at least one camera 21a, 21b, or 21c is likely to see only part of the marker 32 while at least one other camera 21a, 21b, or 21c will see the entire marker. Similarly, the photodetectors 27 will detect unequal intensities of light, as may be determined by circuits which compare the intensities detected by at least two photodetectors 27. Because the photodetectors 27 are mounted slightly outward from the cameras 21a, 21b, 21c, the photodetectors may detect a problematic circumstance before the cameras 21a, 21b, 21c are affected. If all the photodetectors 27 receive approximately the same intensity of light from a marker 32, then in general all cameras will see the entire marker 32. When at least two photodetectors 27 receive substantially different light intensities, the tracker 20 can warn the user of a potentially inaccurate measurement, such as by causing the status light 44 to flash. Similarly, the photodetectors 27 can detect partial blockage of the virtual image of a marker 32. While the photodetectors are optional, they may be used to warn the user of potentially inaccurate results in these problematic circumstances.
Because of the practical area of the mirror 33 may be limited, the embodiments described previously may have a limited range of angles in which the virtual image of the marker 32 in the mirror 33 is fully visible to the tracker 20. This visibility limitation may be partially addressed by moving or rotating the tracker 20 to a different viewpoint, but that may not be convenient or possible while maintaining the coordinate system. To address this limitation, alternative embodiments may be used which have better virtual image visibility. These embodiments operate on the same principle as the foregoing embodiments by maintaining three geometric relationships between the indicator 31, the marker 32, the mirror 33 and the tracker 20:
1. The marker 32 and the indicator 31 have the same distance from the planar reflecting surface of the mirror 33;
2. The line between the marker 32 and the indicator 31 is perpendicular to the reflecting surface of the mirror 33; and
3. The image of the marker 32 in the mirror, though not the marker 32 itself is be directly visible to the tracker 20.
These geometric relationships can be maintained even if part of the probe 30 is hinged or moveable with respect to the base plate 35 or to the rest of the probe 30.
A first of these alternative embodiments is illustrated in
Another probe embodiment is illustrated in which includes semicircular arc 65 coupled to the transparent base plate 35 which includes an indicator 31, and slider 66 coupled to the semicircular arch 65 and a marker 32, a mirror 33 configured to maintain the geometric relationships described above. In this embodiment, the slider 66 includes a marker support 61 that keeps the marker 32 at a constant distance from the mirror 33. The slider 66 maintains contact with the circular arch 65 so that the mirror 33 remains at a constant distance from indicator 31 at the center of the circular arch 65. The slider 66 is designed with guides or grips to keep it in contact with the arch 65 as the slider is moved along the arch 65. The slider 66 and the marker support 61 insure that the marker 32 and the indicator 31 are equidistant from the reflecting surface of mirror 33 and the line 5 between the marker 32 and the indicator 31 remains perpendicular to the mirror 33. Thus, the arch 65, slider 66, and marker support 61 insure that the geometric relationships described above are maintained as the slider 66 and marker support 61 are moved along the arch 65. As such, the embodiment insures that the virtual image of the marker 32 as viewed by a tracker 20 always coincides with the physical location of the indicator 31. While the arch 65 and the indicator 31 remain fixed, the marker support 61 can be moved to an angle where the tracker 20 can have an unobstructed view of the virtual image of the marker 32.
The embodiments illustrated in
A further embodiment of a probe 30 is illustrated in
While the foregoing embodiments are intended for use on a planar surface 12, base plate 35 (or the structural base 63) of a probe 30 need not be planar if the base plate 35 (or the structural base 63) has a surface shape which matches a non-planar measurement surface 12. For example, if the measurement surface 12 is spherical with a radius R, the base plate 35 may have a mating spherically concave surface with a radius R. Such a probe 30 may be useful in manually designating a location on a globe, for example. Similarly, if the surface 12 is cylindrical, the base plate 35 (or the structural base 63) may have a mating, cylindrical curvature.
A further embodiment appropriate for indicating points on a 3D surface is illustrated in
An alternative embodiment of the probe 30 may replace the sharp pointing indicator tip with a spherical tip of known radius. In this case, the indicator 31 is the center of the sphere. The probe 30 would be used in the same way as a spherical sensing tip on a coordinate measuring machine (CMM). That is, the indicator 31 at the center of a sphere never actually touches the surface of some 3D object which is being digitized but maintains a constant distance from the surface. Subsequent software processing adjusts the measured coordinates to account for the offset of the center of the spherical tip from its surface. Digitizing surfaces using a probe with a spherical tip is well known in the art of 3D coordinate measurement.
In the various embodiments, the mirror 33 need not be planar. Instead, a curved mirror 33A may be used as illustrated in
The probe embodiments described so far require only one marker 32 to be tracked. Since the virtual image of the marker 32 is tracked and appears to be exactly at the physical location of the indicator 31, no further markers are required for determining the location of the indicator 31. Consequently, the foregoing probe embodiments are shown as being circular in configuration since their rotational orientation is not of significance. However, if the probe 30 is not rotationally symmetrical for a 2D application (e.g., it can point in the direction of a line as well as reveal the location of a point on the line) or additional information is required regarding the shape of a 3D object (e.g., the normal to the surface) the tracker 20 must be able to determine the angular orientation of the probe 30 as well as the location of the indicator 31. To enable the tracker 20 to obtain this additional information, at least one more marker 32a on the probe 30 may be required. The additional marker or markers 32a, 32b are referred to herein as secondary markers, while the marker 32 whose virtual image coincides with the indicator 31 is referred to herein as the primary marker.
For example,
The location coordinates of the virtual image of the marker 32 and a single secondary marker 32b may be used to determine the orientation of the probe in a 2D coordinate system. In a 3D coordinate system, at least two secondary markers 32a and 32b are required in order to determine its position and orientation with respect to the three dimensions of space plus the three rotational orientations (i.e., pitch, roll and yaw) that the probe 30 can assume. The secondary markers 32a or 32b need not be reflected in the mirror 33 since there is no need to create a virtual image of the markers in order to avoid obscuring the indicator 31. It should be noted that although the primary marker 32 and the secondary marker 32a are shown as being physically located close to each other in
When two or more secondary markers 32a and 32b are positioned on a probe 30, it may be advantageous to provide a way for the tracker 20 to distinguish among them. One way to distinguish multiple markers 32, 32a, and 32b is to insure that they form an irregular pattern so that the measured locations of all the markers 32, 32a, and 32b can exactly match only one orientation. Another way to distinguish among markers is to make them appear different to the tracker 20, such as by means of color, shape or other feature. For example, if the markers 32, 32a, 32b are active LEDs, the LEDs may be flashed in a predetermined sequence or at times controlled by the tracker 20 to uniquely identify each marker. These and other ways of distinguishing markers commonly known in commercially available trackers 20 may be used.
In an embodiment, the probe may be configured so that the tracker can view both the primary marker 32 itself and the virtual image of the primary marker 32 (i.e., the marker 32 as observed in the mirror 33) to provide two separate, spaced-apart markers. In this embodiment, the virtual image of the marker 32 will appear at the same location as the indicator 31, while the marker 32 itself will be imaged at its actual location. For example, in the probe 30 shown in
For each of the single marker embodiments described above, at least one secondary marker 32a or 32b may be added. For example, the embodiment illustrated in
Besides providing orientation information, the secondary markers 32a may also be used to verify the measurements of the primary marker 32. For example, the computed distances between the measured locations of all the markers (primary and secondary) may be compared to the known distances between the markers on a probe 30. If the distances between the measured marker separations differ from the known distances by more than a small tolerance, then a measurement problem is indicated. Such consistency checks are well known to persons of ordinary skill in the art of optical digitizing.
Further, the orientation information provided by the secondary markers may be used to compensate for known orientation-related systematic errors-especially in 3D applications. For example,
While the present invention has been disclosed with reference to certain preferred embodiments, numerous modifications, alterations, and changes to the described embodiments are possible without departing from the sphere and scope of the present invention, as defined in the appended claims. Accordingly, it is intended that the present invention not be limited to the described embodiments, but that it have the full scope defined by the language of the following claims, and equivalents thereof.
