BACKGROUND OF THE INVENTION The present invention relates to methods and apparatuses for laser projection. Moreover, the present invention is directed to machining methods for machining a workpiece using a working machine, and in particular relates to a machining method suitable for confirming 5 a tool attached to a working machine. Machining by an NC (Numerical Control) processing machine automatically proceeds in accordance with an NC program. Once machining starts, the progress of machining in accordance with an NC program is advantageous from a view point of an improvement in machining efficiency and the like, but if there is an error in the NC program, there is a problem 10 that machining will progress without noticing the error. In order to accurately perform machining, an operator of a processing machine may input a correction numerical value in the middle of machining. In this case, for example if the operator inputs a wrong numerical value, there is a risk that wrong machining is performed as is. Furthermore, after all the machining operations are complete, there is a need to determine whether all the drawing-specified regions 15 have been accurately machined. However, for example if there are many regions to be machined, there is a problem that a confirmation work takes time and/or a risk of overlooking an un-machined region. In light of these problems, there are proposed a method and apparatus for determining, by projecting design information on a workpiece with a laser beam and confirming 20 a projected laser locus by a person, whether machining as specified by design has been performed at a design specified position. For example, Kaufman et al. describes, in US Patent No. 6,547,397, a laser drawing apparatus that scans a laser beam with two galvanomirrors. Kaufman et al. also describes, in US Patent No. 7,306,339, a method comprising the steps of projecting a laser beam 25 of a laser drawing apparatus onto a characteristic region of a workpiece; detecting a laser beam spread and reflected from the characteristic region of this workpiece; thereby recognizing a position (reference point on the workpiece) of the characteristic region of the workpiece; thereby recognizing a positional relationship between the workpiece and the laser drawing apparatus; and drawing design information or the like on the workpiece. 30 As a first example of a conventional machining method, for the purpose of removing a drawback of a lot of time required for setting a tool to an ATC (Automatic Tool W6916 - 2 - * Changer) and/or confirming the tool set in the ATC, and for simplifying this confirmation, there ^ is known a working machine's tool management system capable of automatically managing tools without a person and of realizing automation of tool management (e.g., see Japan Patent No. 1931433). Specifically, the working machine's tool management system comprises: a working 5 machine having tools of different shapes; a tool selection/drive control device for selecting a tool of this working machine; a tool recognition device for recognizing the shape of a tool; a central control unit that controls a tool recognition procedure, calculates tool recognition information of this tool recognition device, and controls the tool selection/drive control device; and a tool data generation device for preparing tool selection information, wherein the recognition information 10 by the tool recognition device and tool data of the tool data generation device are compared and managed. Secondly, there are known a tool observation method, a device therefor, and a cutting work system for accurately imaging a tool on machine with a tool observation technique of a cutting work device and for managing the tool based on this image (e.g., see JP-A-2001- 15 269844). Specifically, there is provided the tool observation method comprising the steps of imaging a state of a tool for cutting a workpiece, with an imaging unit; and observing the tool based on this image information, wherein a plurality of images of the workpiece are captured while rotating or moving the tool at least before or after machining the workpiece with the tool, and wherein a focused image among the plurality of images is selectively used for observation. 20 Thirdly, a tool management device in a working machine is known, which eliminates a work for confirming tool storage positions in a tool magazine where a plurality of tools are to be stored, the work being performed by an operator, and which quickly and reliably performs the work for storing the tools into the tool magazine (e.g., see JP-A-2005-324262). Specifically, a normal tool is imaged and stored into a first tool image data storage unit. Next, 25 tool management information including a tool number relating to first tool image data is stored into a first tool management information storage unit. Then, a plurality of tools to be used are randomly mounted on the tool magazine without taking a machining sequence into consideration, and the tools are imaged and stored into a second tool image data storage unit. Further, second tool image data is collated with the first tool image data. If the both data 30 coincide with each other, the tool management information including the tool number of the first tool image data is set as tool management information of the second tool image data. Furthermore, by analyzing a machining program, the storage positions of the tools in the tool magazine are shuffled so as to minimize a total machining time. Fourthly, there is known an apparatus capable of finding automatically and in A W6916 - 3 - advance a mounting mistake of a tool T onto a magazine 1 and flirthermore realizing automatic measurement and automatic correction of a high precision tool T (e.g., see JP-A-6-134638). Specifically, a captured image of the tool Tl is transferred as image information to an image processing unit 8a of a personal computer 8 from an imaging unit 5. This image information is 5 processed in an image processing unit 8a, and then sent to a tool feature quantity calculation unit 8b. The tool feature quantity calculation unit 8b extracts and calculates a feature quantity of the tool Tl from this image data. Then, a collation and recognition unit 8c collates the feature quantity data of the tool Tl extracted and calculated by the tool feature quantity calculation unit 8b with master data PI regarding the tool Tl to recognize whether or not an imaged tool Tl 10 coincides with a tool Tl specified by an NC apparatus 3. SUMMARY OF THE INVENTION However, with the techniques described in US Patent No. 6,547,397 and US Patent No. 7,306,339, a person needs to judge a laser projection result by eye, and such a degree 15 of determination of whether or not machining is omitted is possible by eye. However, it is difficult to accurately determine whether or not a machining position is correct and whether or not a machining dimension is correct. Japan Patent No. 1931433 (corresponding to JP-B-H6-61668 or JP-A-S61- 178141) describes a system which recognizes the shape of a tool set in an ATC and compares and 20 manages the recognized information and the tool data of a tool data generation device, thereby managing the tool, but does not describe a method for determining whether or not a tool used in machining is a desired tool. JP-A-2001-269844 describes a system, in which a tool on machine is accurately imaged, and based on this image, the life of the tool is judged by operator's eyes and/or tool 25 dimensions are measured by image processing, but does not describe a method for determining whether or not a tool used in machining is a desired tool. JP-A-2005-324262 describes a tool management device, in which first a normal tool is imaged to acquire first tool image data, and then tool management information including a tool number related to the first tool image data is added, next a plurality of tools to be used are 30 randomly mounted on a tool magazine without taking a machining sequence into consideration, and a tool after being mounted is imaged to acquire second tool image data, and then the first image data is collated with the second tool image data to automatically determine which tool is stored into which magazine, and thereafter by analyzing a machining program, the storage positions of the tools in the tool magazine are shuffled so as to minimize a total machining time. W6916 • However, JP-A-2005-324262 does not describe a method for determining whether or not a tool used in machining is a desired tool. JP-A-6-134638 describes a tool automatic collation/recognition device having a function to image a tool Tl stored in a magazine and extract and calculate a feature quantity of 5 the tool Tl from image information of the tool Tl, and subsequently collate the feature quantity data of the tool Tl with master data Pi regarding the tool Tl and thereby determine whether or not the imaged tool Tl coincides with the tool Tl specified by the NC unit 3. However, P-A- 6-134638 does not describe a method for determining whether or not a tool used in machining is a desired tool. 10 Then, an object of the present invention is to provide a method and apparatus for not only projecting design information on a workpiece using a laser beam but also easily performing comparative determination between the design information and a machining result on the workpiece. Another object of the present invention is to provide a machining method capable of machining after determining whether or not a tool used in machining is a desired tool. 15 A laser projection method of the present invention includes: a first step of irradiating, from a laser projection unit, a workpiece that is a measurement object, with a laser while controlling a plurality of mirror angles; a second step of imaging the workpiece with a stereo camera, extracting a contour of the workpiece, and calculating a three-dimensional coordinate; a third step of calculating a positional relationship between the laser projection unit 20 and the workpiece by comparing the three-dimensional coordinate of the workpiece contour calculated in the second step with the mirror angle; and a fourth step of performing coordinate transformation of CAD data information and drawing CAD data to the workpiece from the laser projection unit, based on the positional relationship between the laser projection unit and the workpiece calculated in the third step. 25 Moreover, a laser projection apparatus of the present invention comprises: a laser projection unit to irradiate a workpiece that is a measurement object, with a laser while controlling a plurality of mirror angles; an image capturing unit to image the workpiece with a stereo camera and take in a captured image; an image processing unit to extract a contour of the workpiece from the image; a coordinate calculation unit to calculate a three-dimensional 30 coordinate; a relative positional relationship calculation unit to compare a calculated threedimensional coordinate of the contour of the workpiece with the mirror angle and calculate a positional relationship between the laser projection unit and the workpiece; and a CAD data conversion unit to perform coordinate conversion of CAD data information, based on the positional relationship between the laser projection unit and the workpiece calculated by the W6916 - 5 - relative positional relationship calculation unit. ^ Moreover, a machining method of the present invention includes: a first step of selecting a component of a tool; a second step of assembling the component selected in the first step; a third step of imaging the tool assembled in the second step; and a fourth step of 5 determining, by collating a collation image, which is prepared in advance from an image of a tool having a correct component correctly assembled therein, with an image captured after assembly in the third step, whether or not a desired tool has been assembled. With such a method, machining can be performed after determining whether or not a tool used in machining is a desired tool. 10 According to the method and apparatus for laser projection of the present invention, a method and apparatus can be provided, for not only projecting design information on a workpiece using a laser beam but also easily performing comparative determination between design information and a machining result on the workpiece. Moreover, according to the machining method of the present invention, machining can be performed after determining 15 whether or not a tool used in machining is a desired tool. Other objects, features and advantages of the invention will become apparent from the following description of the embodiments of the invention taken in conjunction with the accompanying drawings. 20 BRIEF DESCRIPTION OF THE DRAWINGS FIG 1 is a view showing a system configuration in an embodiment of the present invention. FIG. 2 shows a workpiece having a round hole machined therein. FIG. 3 is a view showing a state where design information is projected on a 25 workpiece prior to machining, in the embodiment of the present invention. FIG. 4 is a view showing a state where design information is projected in the middle of machining a round hole, in the embodiment of the present invention. FIG. 5 is a view showing a state where a cross line is projected on a punch mark, in the embodiment of the present invention. 30 FIG. 6 is a view showing a state where a cross line is projected on a marking start point position and a marking end point position, in the embodiment of the present invention. FIG. 7 is a view illustrating a procedure for comparing an actual contour v^th a projection contour, in the embodiment of the present invention. FIG. 8 is a view illustrating the definition of a remaining amount, in the W6916 - 6 - embodiment of the present invention. FIG. 9 is a view illustrating the definition of a deviation amount, in the embodiment of the present invention. FIG. 10 is a view illustrating an image processing algorithm for extracting a 5 circular contour, in the embodiment of the present invention. FIG. 11 is a view showing a state where an extraction result of the circular contour is superimposed on a stereo-camera image and displayed, in the embodiment of the present invention. FIG. 12 is a view showing a state where only a desired contour is selected from a 10 result of superimposing the extraction result of the circular contour on the stereo camera image and displaying the same, in the embodiment of the present invention. FIG. 13 is a view showing a state where a remaining amount calculation result is indicated on a workpiece by a text, in the embodiment of the present invention. FIG. 14 is a view showing a state where a deviation amount calculation result is 15 indicated on a workpiece by a text, in the embodiment of the present invention. FIG. 15 is a view illustrating a procedure for recognizing a positional relationship among a stereo camera, a workpiece, and a laser projector, in the embodiment of the present invention. FIG. 16 is a view showing a state where a calculation result of the three- 20 dimensional coordinate of a laser bright spot is displayed on a display, in the embodiment of the present invention. FIG. 17 is a view illustrating a procedure (which a user manipulates while watching a monitor screen) for calculating the three-dimensional coordinate of a circular reference marker or a projection laser bright spot, in the embodiment of the present invention. 25 FIG. 18 is another view illustrating the procedure (which a user manipulates while watching a monitor screen) for calculating the three-dimensional coordinate of a circular reference marker or a projection laser bright spot, in the embodiment of the present invention. FIG. 19 is a view illustrating a procedure (which a user manipulates while watching a monitor screen) for calculating the three-dimensional coordinate of a reference 30 position (a feature shape) of a workpiece, in the embodiment of the present invention. FIG. 20 is a view showing a state where a result of calculating the reference position of a workpiece with a stereo camera is displayed on a display, in the embodiment of the present invention. FIG. 21 is a view showing a state where a result of converting a resuh of W6916 - 7 - © calculating the reference position of a workpiece with the stereo camera to a reference position seen from a laser projection unit is displayed on a display, in the embodiment of the present invention. FIG. 22 is a block diagram showing the entire configuration of a working machine 5 for performing a machining method according to an embodiment of the present invention. FIG. 23 is a flowchart showing an operation of a computer for NC program used for the working machine that performs the machining method according to an embodiment of the present invention. FIG. 24 is a flowchart showing an operation of a tool assembly unit, a tool image 10 information acquisition unit, and a tool image information determination unit used for the working machine that performs the machining method according to an embodiment of the present invention. FIG 25 is a flowchart showing the content of a method for capturing a tool image for collation in the working machine that performs the machining method according to an 15 embodiment of the present invention. FIG. 26 is an explanatory view of the method for capturing a tool image for collation in the working machine that performs the machining method according to an embodiment of the present invention. FIG. 27 is a front view of a tool used for the working machine that performs the 20 machining method according to an embodiment of the present invention. FIG. 28 is a front view of a tool used for the working machine that performs the machining method according to an embodiment of the present invention. FIG. 29 is a front view of a tool used for the working machine that performs the machining method according to an embodiment of the present invention. 25 FIG. 30 is a front view of a tool used for the working machine that performs the machining method according to an embodiment of the present invention. FIG. 31 is a flowchart showing an operation of a tool measurement unit in the working machine that performs the machining method according to an embodiment of the present invention. 30 FIG. 32 is an explanatory view of shape data of a tool used for the working machine that performs the machining method according to an embodiment of the present invention. FIG. 33 is an explanatory view of shape data of a tool used for the working machine that performs the machining method according to an embodiment of the present W6916 - 8 - • invention. FIG. 34 is an explanatory view of shape data of a tool used for the working machine that performs the machining method according to an embodiment of the present invention. 5 FIG. 35 is an explanatory view of shape data of a tool used for the working machine that performs the machining method according to an embodiment of the present invention. FIG. 36 is a flowchart showing an operation to attach tool information to a tool and confirm the tool in the working machine that performs the machining method according to 10 an embodiment of the present invention. FIG. 37 is an explanatory view of how to attach tool information to a tool in the working machine that performs the machining method according to an embodiment of the present invention. FIG. 38 is an explanatory view of how to attach tool information to a tool in the 15 working machine that performs the machining method according to an embodiment of the present invention. FIG. 39 is an explanatory view of how to attach tool information to a tool in the working machine that performs the machining method according to an embodiment of the present invention. 20 FIG. 40 is an explanatory view of how to confirm a tool in the working machine that performs the machining method according to an embodiment of the present invention. FIG 41 is an explanatory view of how to confirm a tool in the working machine that performs the machining method according to an embodiment of the present invention. FIG. 42 is an explanatory view of how to confirm a tool in the working machine 25 that performs the machining method according to an embodiment of the present invention. FIG 43 is an explanatory view of how to confirm a tool in the working machine that performs the machining method according to an embodiment of the present invention. FIG 44 is a flowchart showing an operation to store a tool in the working machine that performs the machining method according to an embodiment of the present 30 invention. FIG. 45 is a flowchart showing the content of a machining procedure performed by the working machine that performs the machining method according to an embodiment of the present invention. W6916 _. DESCRIPTION OF THE EMBODIMENTS ^ A method and apparatus for laser projection of the present invention relate to methods and apparatuses for drawing design information on a workpiece using a laser beam. Hereinafter, an embodiment of the method and apparatus for laser projection of the present 5 invention is described using FIG. 1 to FIG. 20. FIG. 1 shows the entire configuration of a laser projection system having a coordinate detection flinction in the embodiment of the present invention. A laser source 1 is coupled to a laser control unit 10, and is supplied with electric power fi"om a laser power supply 23 via the laser control unit 10. Moreover, the laser source 1 oscillates or stops in accordance 10 with an instruction from a mirror position indication/detection unit 15. As a specific example, for example in drawing two circles, in the middle of moving from a first circle to a second circle, the oscillation of a laser is stopped so that two circles are drawn individually. A laser beam 200 oscillated from the laser source 1 is focused by a focusing lens 3 at a desired distance. In order to focus the beam at a desired distance, the focusing lens 3 is 15 mounted on a linearly-moving stage 2 that linearly moves in an optical axis direction. The position of the linearly-moving stage 2 is controlled by a linearly-moving stage control unit 11. Specifically, the position of the linearly-moving stage is calculated and controlled by a linearlymoving stage position indication/detection unit 14 so that the laser beam is focused at a laser drawing position determined by a CAD (Computer Aided Design) data conversion unit 21 to be 20 described later and so that the linearly-moving stage moves to a calculated position. Note that the linearly-moving stage 2 is supplied with electric power from a motor drive power supply 25 via the linearly-moving stage control unit 11. Moreover, the linearly-moving stage control unit 11 is supplied electric power also from a circuitry power supply 24. A focused beam 201 emitted from the focusing lens 3 is projected on a workpiece 25 via a first galvanomirror 4 and a second galvanomirror 5. The angles of the first galvanomirror 4 and second galvanomirror 5 are controlled by a first angle control unit 12 and a second angle control unit 13, respectively. Specifically, a first angle and a second angle are calculated by the mirror position indication/detection unit 15 so that the focused beam 201 travels toward a laser drawing position determined by the CAD data conversion unit 21 to be described late, and the 30 first galvanomirror 4 and the second galvanomirror 5 are controlled so as to rotate to the calculated angles, respectively. The first galvanomirror 4 and the second galvanomirror 5 are supplied with electric power from the motor drive power supply 25 via the first angle control unit 12 and the second angle control unit 13. Moreover, the first angle control unit 12 and the second angle control unit 13 are supplied with electric power also from the circuitry power W6916 -10- supply 24. ^ ^ Next, a coordinate detection unit is described. In this embodiment, the coordinate detection unit comprises a stereo camera. A stereo camera 8 comprises a left camera 6 and a right camera 7. Images captured by the left camera 6 and the right camera 7 are 5 acquired into a computer 23 via an image capturing unit 17. The acquired image is processed by an image processing unit 18, where contour extraction and the like to be described later are performed. Subsequently, a three-dimensional coordinate of an extracted contour is calculated by a coordinate calculation unit 19. Here, the current positions (angles) of the first angle control unit 12 and second 10 angle control unit 13 are continuously detected by the mirror position indication/detection unit 15. In a relative positional relationship calculation unit 20, the three-dimensional coordinate extracted by the coordinate calculation unit 19 is compared with the angles detected by the mirror position indication/detection unit 15 so as to calculate a relative positional relationship between the laser projection unit 9 and the stereo camera 8, a positional relationship between the 15 stereo camera 8 and a workpiece 26, and fiirthermore a positional relationship between the laser projection unit 9 and the workpiece 26. In the CAD data conversion unit 21, based on the relative positional relationship between the laser projection unit 9 and the workpiece 26 calculated by the relative positional relationship calculation unit 20, information of CAD data 22 is subjected to coordinate conversion, thereby generating data that is drawn on the workpiece by 20 the laser projection unit 9. Next, this embodiment is described using FIG. 2 to FIG. 14. FIG. 2 shows the workpiece 26 having two cylindrical bores machined at two places therein. The contours of the cylindrical bores are referred to as workpiece contours 24a and 24b. 25 FIG. 3 shows the workpiece 26 before the cylindrical bore is machined. Design data projected on the workpiece 26 is a projection contour 25. In this way, by projecting design data on an actual workpiece prior to machining, a final image of machining can be confirmed on an actual workpiece prior to machining. This is one of the effects of this embodiment. FIG. 4 shows the workpiece 26 having therein the cylindrical bore halfway 30 machined. By comparing the workpiece contour 24a with the projection contour 25, a machining remaining amount can be visually confirmed on an actual workpiece. This is one of the effects of this embodiment. FIG. 5 shows a state where a cross line 27 is drawn at a punch mark 28 indicative of a machining position. In an NC processing machine, the NC processing machine itself W6916 - 11- punches prior to processing. As shown in FIG. 5, a machining position in design is projected to ^ ^ the machining punch mark 28, e.g., in the case of cylindrical bore machining, the cross line 27 is projected to the center of a circle, so that it can be determined prior to machining whether or not a machining punch position, i.e., a machining position input to an NC program, coincides with a 5 position indicated by design, and thus wrong cutting, i.e., machining at a different position, can be obviated. FIG. 6 shows a state where cross lines 27a and 27b are drawn, respectively, at a start point 28a and an end point 28b of a marking-offline serving as a reference for a machine work, respectively. By marking off with two intersections of these cross lines 27a and 27b as 10 targets, it is possible to mark off at a correct position relative to a design-specified position. Alternatively, by determining, after marking off, whether or not two intersections of the cross lines 27a and 27b are on the marking-offline, whether or not the marking-offline has been drawn at a correct position relative to a design-specified position can be determined. In FIG. 7, a specific procedure for detecting a machining remaining amount and a 15 machining positional deviation amount is described. First, an image is captured with the left camera and the right camera while laser drawing is turned off (LI, Rl). Then, the contour of a workpiece is extracted (L2, R2), stereo matching is performed (LRl) after performing parallax correction (L3, R3), and the three-dimensional coordinate of the workpiece contour is calculated (LR2). Next, while laser drawing is turned on, an image is captured with the left camera and 20 the right camera (L4, R4). Then, a difference image from the image, which is captured while laser drawing is turned off, is generated (L5, R5), and then stereo matching is performed (LR3) after performing parallax correction (L6, R6), and the three-dimensional coordinate of a laser drawing locus is calculated (LR4). Finally, by comparing the calculated three-dimensional coordinate of the workpiece contour with the three-dimensional coordinate of the laser drawing 25 locus (LR5), a remaining amount and/or a machining positional deviation amount can be calculated (LR6). The remaining amount may be defined as shown in FIG. 8, for example. Moreover, the machining positional deviation amount may be defined as shown in FIG. 9. Here, in order to extract an arc contour of a cylindrical bore, processing shown in 30 FIG. 10 may be performed, for example. Specifically, first a captured image (FIG 10A) is binarized (FIG. lOB), and subsequently a connected component is calculated (FIG. IOC). Specifically, area selection based on a shape feature quantity (in this embodiment, elliptic arc) will be performed. Next, the shape of the selected area is converted to a minimum circumscribed circle (FIG. lOD). Furthermore, the area is expanded with a circular structural W6916 - 12- element (FIG. lOE). Note that, in FIG. lOE, only two arcs are expressed, but actually in FIG. ^ IOC the areas are finely selected, and therefore actually there are the same number of circular structural elements as the number of the selected areas. Then, a sum area of all areas is calculated (FIG. lOF). Then, as shown in FIG. lOQ an area (analysis area) including a desired 5 workpiece contour is narrowed down. Subsequently, within this analysis area, the image is divided by threshold value processing (FIG. lOH), and further divided into line segments and elliptic arcs (including arcs) (FIG. 101), and the contours present on the the same circle are connected (FIG. lOJ). Specifically, processing is performed, in which an ellipse is applied to the divided line segments and arcs, and the one whose center position and radius are within a 10 certain range is regarded as the same circle. With the above-described processing, a desired workpiece contour can be extracted. In order for an operator to perform such processing, for example as shown in FIG. 11 the image may be displayed on a monitor 29 and when an operator depresses a contour extraction button 107, the above-described contour extraction processing may be performed and 15 an extraction result may be displayed so as to be superimposed on the image. Here, if a plurality of (two, in the example of FIG. 11) desired workpiece contours have been extracted, then as shown in FIG. 12 a desired contour may be selected with a mouse pointer 102a. The laser projection unit can also draw a text, and therefore as shown in FIG. 13 and FIG. 14, the remaining amount and the deviation amount can be directly drawn on a 20 workpiece so as to be able to visually teach an operator In this manner, by visually showing the remaining amount and the deviation amount to an operator, not only the design information can be projected on a workpiece using a laser beam, but also comparative determination between design information and a machining result on a workpiece can be easily performed. Next, using FIG. 15, a method is described, for calculating a relative positional 25 relationship between the stereo camera 8 and the laser projection unit 9. First, a laser beam is projected to an adequate position on a workpiece (FIG. 15a). At this time, the angles of the first and second galvanomirrors are grasped by the mirror position indication/detection unit 15 (FIG 15b). Then, the three-dimensional coordinate of a laser bright spot on the workpiece is measured with the stereo camera 8 (FIG. 15c). The above-described 30 work (Step 1) is repeated three times. The above-described work may be performed four times or more as required. Then, as shown in FIG. 16, at three or more positions, a relationship between a coordinate seen fi"om the point of origin of the stereo camera and a coordinate seen fi-om the point of origin of the laser projection unit 9 can be calculated. Here, the point of origin of the stereo camera 8 is a lens center of the left camera 6, for example. The point of W6916 - 1 3 - » origin of the laser projection unit is a mirror center of the first galvanomirror. Here, the center ^ of rotation of the first galvano mirror and the center of rotation of the second galvanomirror deviate from each other, but the detailed description thereof is omitted because a two-angle specified projection method taking into consideration a deviation is formulated in US Patent No. 5 7,306,339. In the laser projection unit 9, only two angles, i.e., a first angle 0n and a second angle (pm, are specified, and therefore it is not possible to know at which distance a workpiece has been irradiated with a projected laser beam. That is, only with information of a point PI (61, (pi) (rl is uncertain), a point P2 (92, (p2) (r2 is uncertain), and a point P3 (03, (p3) (r3 is 10 uncertain), it is not possible to determine where a work surface is. However, at the same time PI (xl, yl, zl), P2 (x2, y2, z2), and P3 (x3, y3, z3), which are the three-dimensional coordinates of the points PI, P2, and P3, are grasped by the stereo camera 8, and therefore if these relationships are used, rl, r2, and r3 can be uniquely calculated. Thus, at the same time, a relative positional relationship between the stereo camera 8 and the laser projection unit 9 can be 15 also calculated (FIG. 7f). Specifically, first, (9n, 9n, m) is converted to a rectangular coordinate system. PI: (01, 9I, rl)—> (rl-COS01-cos(pl, rl-cos01-sin9l, rl-sin9l) P2: (02, (p2, r2) -^ (r2- cos02- cos(p2, r2- cos02- sin(p2, r2- sin(p2) P3: (03, {p3, r3)—>• (r3-COS03 cos(p3, r3-cos03-sin{p3, rl-sin93) 20 Here, unknown values are rl, r2, and r3. On the other hand, the coordinates of the laser bright spots seen fi-om the stereo camera are as follows. P l : ( x l , y l , z l) P2: (x2, y2, z2) 25 P3:(x3,y3,z3) Here, because the distances between the respective points are the same both in a coordinate system of the laser projector and in a coordinate system of the stereo camera, the following formulas are established. |Pl-P2|=|pl-p2| 30 |P2-P3|=|p2-p3| |P3-PlHp3-pl| As described above, because there are three formulas for three unknown values, the unknown values, rl, r2, and r3, can be uniquely calculated. Now assume that the coordinates of the laser bright spots in the stereo camera coordinate system are (xl, yl, zl), (x2, y2, z2), and (x3, y3, z3). W6916 - 14- ^ and that the coordinates of the laser bright spots in the laser projector coordinate system are (XI, ^^ Yl, Zl), (X2, Y2, Z2), and (X3, Y3, Z3). Then, the circumcenter of (xl, yl, zl), (x2, y2, z2), and (x3, y3, z3) is calculated, and this is designated by (xO, yO, zO). Next, the circumcenter of (XI, Yl, Zl), (X2, Y2, Z2), and (X3, Y3, Z3) is calculated, and this is designated by (XO, YO, 5 ZO). Here, a vector heading toward the circumcenter (xO, yO, zO) from the point of origin of the stereo camera coordinate system is designated by A. A vector heading toward the circumcenter (XO, YO, ZO) from the point of origin of the laser projector coordinate system is designated by B. Although seen from the different coordinate systems, (xO, yO, zO) and (XO, YO, ZO) are the the same points in a global coordinate system. Then, this point is set to the point of origin of the 10 global coordinate system. Then, a vector heading toward the point of origin of the stereo camera coordinate system from the point of origin of the global coordinate system is -A, and a vector heading toward the point of origin of the laser projector coordinate system from the point of origin of the global coordinate system is -B. Accordingly, the positional relationship between the stereo camera coordinate system and the laser projector coordinate system can be 15 easily calculated from the vector -A and the vector -B. Note that, if two or more laser spots reside on the same straight line when laser bright spots are seen from the stereo camera and the laser projector, the mutual positional relationship cannot be calculated, and therefore the laser bright spots should not reside on the same straight line when seen from whichever coordinate system. 20 Next, a specific procedure for calculating the three-dimensional coordinate of a laser bright spot position on the workpiece with the stereo camera 8 is described using FIG. 17 and FIG. 18. First, on the monitor 29, for example an image of the left camera 6 is displayed. Once a vicinity of a reference marker (laser origin) 101 of the workpiece 26 is specified with a mouse pointer 102a, an enlarged window 103 a is displayed. If a circle extraction button 105 is 25 depressed in advance, the image processing unit 18 will extract a laser bright spot (in a circular form) in an enlarged and displayed area (analysis area) and calculate the center of gravity of the circle. In order to confirm that a desired center of gravity has been calculated, the center of gravity position of the circle may be displayed, for example, with a circle, a cross line 104a, and the like. In this system, because the configuration of a stereo camera is employed, the 30 coordinate calculation unit 19 calculates the three-dimensional coordinate of the position of a laser bright spot using a stereo matching approach. For the calculated three-dimensional coordinate, a calculated coordinate value 108a may be displayed. In addition, first and second angle values 109a may be displayed. In FIG. 17, the analysis area is narrowed down by clicking a vicinity of the W6916 - 15- _- reference marker 10a with the mouse, but as shown in FIG. 18, the analysis area may be ^^ narrowed down by drawing a square 110 with the mouse. Next, a specific procedure for calculating, with the stereo camera 8, a position serving as a reference on the workpiece, for example such as the three-dimensional coordinate of 5 a feature point, such as a reference marker, and a comer, is described using again FIG. 17 and FIG. 18, and furthermore FIG. 19. First, on the monitor 29, an image of the left camera 6 is displayed, for example. This time, the circle 101 in FIG. 17 and FIG. 18 is regarded as a reference marker Once a vicinity of the reference marker 101 is indicated with the mouse pointer 102a, the enlarged window 103 a is displayed. If a circle extraction button 105 is 10 depressed in advance, the image processing unit 18 will extract the reference marker 101 (in a circular form) in an enlarged and displayed area (analysis area) and calculate the center of gravity of the circle. In order to confirm that a desired center of gravity has been calculated, the center of gravity position of the circle may be displayed, for example, by a circle, a cross line 104a, and the like. In this system, because the configuration of a stereo camera is employed, 15 the coordinate calculation unit 19 calculates the three-dimensional coordinate of the reference marker using a stereo matching approach. For the calculated three-dimensional coordinate, the calculated coordinate value 108a may be displayed. In addition, the first and second angle values 109a may be displayed. As shown in FIG. 19, even without the reference marker 101, if a workpiece itself 20 has a place 114, for example such as a comer 114 whose coordinate is known, there is a method, for example, comprising the steps of depressing a comer extraction button 106 in advance; selecting a vicinity of the comer with a mouse and thereby automatically recognizing the comer; and calculating the three-dimensional coordinate of the comer. With the above processing, as shown in FIG. 20 a positional relationship between 25 the workpiece 26 and the stereo camera 8 can be calculated. Subsequently, if the recognized positional relationship between the stereo camera 8 and the laser projection unit 9 is used, a positional relationship between the workpiece 26 and the laser projection unit 9 is also uniquely calculated. By performing coordinate conversion of the CAD data 22 by the CAD data 30 conversion unit 21 in accordance with this positional relationship between the workpiece 26 and the laser projection unit 9, the data for laser projection is generated. Based on this data for laser projection, the stage position indication/detection unit 14 and the mirror position indication/detection unit 15 drive the linearly-moving stage 2, the first galvanomirror, and the second galvanomirror via the linearly-moving stage control unit 11, the first angle control unit W6916 - 16- « ^ 12, and the second angle control unit 13 to draw. ^ The method and apparatus for laser projection of the present invention are laser projection techniques effectively utilized in order to obviate v^ong cutting, confirm processing states, and check omission of machining in machine works. 5 Hereinafter, a machining method according to an embodiment of the present invention is described using FIG. 22 to FIG. 45. First, using FIG. 22, the entire configuration of a working machine having a wrong-cutting preventing function based on tool recognition, for performing the machining method according to this embodiment is described. 10 FIG. 22 is a block diagram showing the entire configuration of the working machine for performing the machining method according to an embodiment of the present invention. In the working machine of this embodiment, registered tool image information is already stored in a database 31. A computer for NC program 32 includes an NC program 15 generation unit 33 and an NC program simulator 34. The details of each of these components will be described later using FIG. 23. In a tool assembly unit 311, a tool taken out from a tool storage unit 310 is assembled. A tool image information acquisition unit 312a acquires image information of a tool assembled by the tool assembly unit 311. Then, a tool image information determination 20 unit 313a compares the image information acquired by the tool image information acquisition unit 312a with the registered tool image information taken out from the database 31 to determine the tool. The details of the operation of the tool image information acquisition unit 312a and the tool image information determination unit 313a are described later using FIG. 24. A tool measurement unit 37 includes an NC simulator's tool shape data generation 25 unit 8 and a tool-dimension measurement unit 39. The details of each of these components will be described later using FIG. 27. A computer for tool measurement unit 36 prepares a label by a label printer 314, and also prepares a tag by a tag writer 315. A tool's label/tag attaching unit 316 attaches the prepared label and tag to a tool. 30 A tool information read unit A 317 reads information from the label/tag attached to the tool. The tool image information acquisition unit A 312a acquires the image information of the tool. A tool image information determination unit B 313b determines the tool from the image information acquired by the tool image information acquisition unit A 312a. A comprehensive determination unit A 345a comprehensively determines from the information W6916 - 17- read by the tool information read unit A 317 and the information acquired by the tool image ^ information determination unit B 313b. A comprehensive information generation unit A 346a generates comprehensive information obtained by putting together the information recorded on the label/tag and the image information, and sends the same to the database. 5 An NC control working machine (MC) 344 with an ATC includes a machine's Xaxis/ Y-axis/Z-axis control unit 328, a tool information read unit C 329, a tool image information acquisition unit C 330, an NC control panel 331, a communication terminal unit 332, and an automatic tool change unit (ATC) 318. The automatic tool change unit (ATC) 318 includes a tool information read unit B 319, a tool storage unit 320, an ATC arm 321, and an ATC control 10 unit 322. The NC control working machine (MC) 344 is controlled by a computer for ATC/MC 347. Next, using FIG. 23, the operation of the computer for NC program 32 used in the working machine that performs the machining method according to this embodiment is described. 15 FIG. 23 is a flowchart showing the operation of the computer for NC program used in the working machine that performs the machining method according to an embodiment of the present invention. In machining a workpiece, first in Step SI00, by an NC programmer, an NC program is generated in the NC program generation unit 33 of the computer for NC program 32. 20 Next, in Step SI 10, simulation of the NC program to be executed by the working machine 344 is performed by the NC program simulator 34 of the computer for NC program 32, and in Step SI20, an error, collision hazard prevention, and the like are checked. An NC program confirmed as not having a problem is stored into the database 31 via a network in Step S130. Next, using FIG. 24, the operation of the tool assembly unit 311, the tool image 25 information acquisition unit 312a, and the tool image information determination unit 313a used for the working machine that performs the machining method according to this embodiment is described. FIG. 24 is a flowchart showing the operation of the tool assembly unit, the tool image information acquisition unit, and the tool image information determination unit used for 30 the working machine that performs the machining method according to an embodiment of the present invention. First, in Step S200, a desired tool is selected from the tool storage unit 310 by a working machine's operator. A selected tool is moved to the tool assembly unit 311, and is then assembled by the tool assembly unit 311 in Step S210. Next, in Step S220, an image of the W6916 -18- assembled tool is captured by the tool image information acquisition unit 312a. ^ Here, using FIG. 25 to FIG. 30, a method for capturing a tool image for collation in the working machine that performs the machining method according to this embodiment is described. 5 FIG. 25 is a flowchart showing the content of the method for capturing a tool image for collation in the working machine that performs the machining method according to an embodiment of the present invention. FIG. 26 is an explanatory view of the method for capturing a tool image for collation in the working machine that performs the machining method according to an embodiment of the present invention. FIG. 27 to FIG. 30 are front views of 10 various types of tools used for the working machine that performs the machining method according to an embodiment of the present invention. First, in Step S220A in FIG 25, a tool is installed on a turntable. Next, in Step S220A, the tool is imaged. Here, FIG. 27 shows an example of the appearance of an end mill. FIG. 28 15 shows an example of the appearance of a radius end mill. FIG. 29 shows an example of the appearance of a ball end mill. Furthermore, FIG. 30 shows an example of the appearance of a face mill. Even if these tools are of the the same types, the number of cutting edges may differ. Here, in capturing an image, as shown in FIG. 26 if a tool is imaged only from a certain direction, portions not included in an image will remain. For example, in the case of a 20 cylindrical drill 341, only portion in the range of angle 6 from the center can be imaged. Accordingly, a difference in the number of cutting edges or the like cannot be recognized. Then, in Step 220D of FIG. 25, the tool is rotated and an image thereof is captured. Then, this is repeated via Step S220C to capture an entire circumference image of the tool, and in Step S220E the captured image is registered with the database 31. 25 Note that, this embodiment shows an example, in which the entire circumference image of a tool is captured in capturing an image for registration, and when an assembled tool is imaged, an image is captured from one direction and one image captured after assembly is collated with a plurality of registered images. Next, returning to Step 230 of FIG. 24, a registered image, which is registered in 30 advance with the database 31, is read. Then, in Step S240, in the tool image information determination unit 313a, the captured tool image is collated with the registered image. If the both coincide, the collation is complete in Step S260, and if not, collation with the next registered image is performed in Step S250. When it has not been determined that the both coincide even if collation with all ^ W6916 -19- the registered images is complete, a wrong tool has been assembled and therefore the tool is reconfirmed and re-assembled. Here, the method for collating images, i.e., comparing the coincidences between images, in Step S240 in FIG. 24 is described. As the method for comparing coincidences 5 between images, a template matching is used for example. As an evaluation value (similarity or dissimilarity) indicative of how much a registered image (template) and a captured image are alike, the following values are used. In Formula (1) to Formula (8) below, a brightness value of a template is designated by T(i, j), and a brightness value of a captured image is designated by I(i, j). For the coordinate (i, j), when the width of the template corresponds to m pixels and the 10 height corresponds to n pixels, the upper left is set to (0, 0) and the lower right is set to (m-1, n- 1). For SSD (Sum of Squared Difference) shown in Formula (1), a template is rasterscarmed, and a square sum of differences between the brightness values of a pixel at the same position is used. The smaller the value of SSD, the more alike the positions become. 15 Formula (1) For SAD (Sum of Absolute Difference) shown in Formula (2), a template is raster-scanned, and a sum of the absolute values of differences between the brightness values of a pixel at the same position is used. The smaller the value of SAD, the more alike the positions 20 become. Formula (2) ^SAD=T'T^Hhj)-TiLj)\ ...(2) >=C (=0 For normalized cross-correlation (NCC) shown in Formula (3), as similarity between a template image and a captured image, a normalized cross-correlation below is used. 25 The closer to 1 the similarity, the more alike the positions become. Formula (3) .V - I .V - 1 : z • 5 i. X Z Hi.jyrii.j) R ^.^^ . . _ , ^ : j " .v-i.v-1 =" •••(3) Jz Z ^(^i)' ^Z Z ^o.j)' This calculation formula is the same as a formula obtained by transforming a formula of an inner product to a formula of Cos6=. If the formula above is transformed to ^ W6916 -20- Formula (4) below, an inner product of a vector of I of MxN dimensions and a vector of T of MxN dimensions is obtained. Formula (4) 7(0.0)7(0,0) -r^ /(L0)r(l..O) I(M -1., X- l)T(M - L .V- 1) •