WO1996028927A1 - Procede et systeme de translation entre une image et un relief tridimensionnel - Google Patents

Procede et systeme de translation entre une image et un relief tridimensionnel Download PDF

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Publication number
WO1996028927A1
WO1996028927A1 PCT/AU1996/000139 AU9600139W WO9628927A1 WO 1996028927 A1 WO1996028927 A1 WO 1996028927A1 AU 9600139 W AU9600139 W AU 9600139W WO 9628927 A1 WO9628927 A1 WO 9628927A1
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WO
WIPO (PCT)
Prior art keywords
dimensional
relief
value
pixel
image
Prior art date
Application number
PCT/AU1996/000139
Other languages
English (en)
Inventor
David Russell Herbert
Original Assignee
David Russell Herbert
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by David Russell Herbert filed Critical David Russell Herbert
Priority to AU48716/96A priority Critical patent/AU4871696A/en
Publication of WO1996028927A1 publication Critical patent/WO1996028927A1/fr

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Classifications

    • BPERFORMING OPERATIONS; TRANSPORTING
    • B44DECORATIVE ARTS
    • B44CPRODUCING DECORATIVE EFFECTS; MOSAICS; TARSIA WORK; PAPERHANGING
    • B44C1/00Processes, not specifically provided for elsewhere, for producing decorative surface effects
    • B44C1/22Removing surface-material, e.g. by engraving, by etching
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00Programme-control systems
    • G05B19/02Programme-control systems electric
    • G05B19/42Recording and playback systems, i.e. in which the programme is recorded from a cycle of operations, e.g. the cycle of operations being manually controlled, after which this record is played back on the same machine
    • G05B19/4202Recording and playback systems, i.e. in which the programme is recorded from a cycle of operations, e.g. the cycle of operations being manually controlled, after which this record is played back on the same machine preparation of the programme medium using a drawing, a model
    • G05B19/4205Recording and playback systems, i.e. in which the programme is recorded from a cycle of operations, e.g. the cycle of operations being manually controlled, after which this record is played back on the same machine preparation of the programme medium using a drawing, a model in which a drawing is traced or scanned and corresponding data recorded
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00Program-control systems
    • G05B2219/30Nc systems
    • G05B2219/35Nc in input of data, input till input file format
    • G05B2219/35533Use, input 2-D data, sectional profile to machine 3-D surface
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00Program-control systems
    • G05B2219/30Nc systems
    • G05B2219/49Nc machine tool, till multiple
    • G05B2219/49007Making, forming 3-D object, model, surface
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00Program-control systems
    • G05B2219/30Nc systems
    • G05B2219/49Nc machine tool, till multiple
    • G05B2219/49235Control depth as function of grey level of scanned object, map of thickness

Definitions

  • This invention relates to computer controlled translation between an image and a three dimensional relief.
  • this invention provides a method, an apparatus, and software for producing an engraving from a colour or monochrome image, and for producing a two dimensional graphic representation of a three dimensional object.
  • this invention provides a method of treating an object to colour or otherwise treat a three dimensional relief or two dimensional representation of a two dimensional graphic.
  • the invention resides in an apparatus and method for the utilisation of computer graphic files comprising a flat two dimensional graphic having two dimensions (herein referred to as the x axis and the y axis) and a light value for each valid x and y co-ordinate, and producing a third dimension value which co-relates to the light value, for each valid x and y co-ordinate, for treating a material in a predetermined manner and in accordance with the third dimension value.
  • a flat two dimensional graphic having two dimensions (herein referred to as the x axis and the y axis) and a light value for each valid x and y co-ordinate, and producing a third dimension value which co-relates to the light value, for each valid x and y co-ordinate, for treating a material in a predetermined manner and in accordance with the third dimension value.
  • a method for producing a three dimensional relief or material surface treatment from a two dimensional image comprising a two dimensional array of pixels said method including:-
  • said light value is a chrominance or luminance value for each pixel.
  • said light value is a grey scale value for each pixel.
  • said method includes traversing said stratum of material in a raster sweep while performing said forming operation.
  • a method for producing a two dimensional image from a three dimensional relief of a stratum of material including:
  • said light value is a chrominance or luminance value for each pixel.
  • said light value is a grey scale value for each pixel.
  • said scanning includes performing a raster scan on said stratum of material and electronically recording measurement data in respect of said elevation variables.
  • said scanning utilises laser measurement of the relief.
  • a method for reproducing a three dimensional relief of a stratum of material including:-
  • translation means for translating between an image comprising a two dimensional array of pixels, and a three dimensional relief or material surface treatment
  • said translation means being adapted to translate between an elevation or depth values at a position in or on said material in response to and in proportion with a light value values for a pixel in a corresponding position in said image.
  • an apparatus for translating a two dimensional image comprising a two dimensional array of pixels to produce a three dimensional relief or a material surface treatment on a stratum of material including:
  • data processing means for receiving light value data in respect of each pixel of the two dimensional array of pixels; material forming or treatment means interfaced with said data processing means for performing a forming or surface treatment operation on a stratum of material;
  • said data processing means positioning said material forming or treatment means relative to the stratum of material in corresponding position to said pixel being processed;
  • translation means to sequentially translate said light value data received by said data processing means proportionally to an elevation value for elevating said material forming or treatment means relative to the stratum of material at said corresponding positions.
  • said light value is a chrominance or luminance value for each pixel.
  • said light value is a grey scale value for each pixel.
  • an apparatus for producing a two dimensional image from a three dimensional relief of a stratum of material including:-
  • translation means to translate said elevation values to light values to constitute data values for individual pixels of the two dimensional image at positions corresponding to said positions across the relief;
  • a computer control system including software for translating between a two dimensional graphic comprising a two dimensional array of pixels, and a three dimensional relief or material surface treatment; said software including a translation algorithm for translating between a light value for each pixel and an elevation value in said three dimensional relief at a position corresponding to the pixel position in said two dimensional array.
  • said light value is a chrominance or luminance value for each pixel.
  • said light value is a grey scale value for each pixel.
  • said software includes a scanning algorithm to raster scan two dimensions of said three dimensional relief, to enable an operation to be performed on or in said three dimensional relief.
  • an apparatus for interconverting between a two dimensional image and a three dimensional relief and/or a material surface treatment to produce a three dimensional surface and/or a treated surface from a two dimensional graphic or to produce a two dimensional graphic from a three dimensional relief or to colour a two or three dimensional representation of a two dimensional graphic comprising data processing means programmed to form a computer control system in accordance with the seventh aspect of the invention, and interface means to material treatment apparatus.
  • Figures 2, 3, and 4 are parts making up the flowchart for the TranslatePass Subroutine, callable from the main program;
  • FIG. 5 is a flowchart for the BmWrite Subroutine, callable from the TranslatePass Subroutine
  • Figure 6 is a flowchart for the SkipOver Subroutine, callable from the TranslatePass Subroutine
  • Figure 7 is a cross section through the x and z axes of an engraved workpiece showing part of the workpiece profile generated using the software according to the invention
  • Figure 8 is a cross section through the x and z axes of an engraved workpiece showing part of the workpiece profile generated using the software according to the invention, but invoking a mirror image function embodied in the software;
  • Figure 9 is a cross section through the x and z axes of an engraved workpiece showing part of the workpiece profile generated using the software according to the invention, but invoking a negative image function embodied in the software;
  • Figure 10 is a cross section through the x and z axes of an engraved workpiece showing part of the workpiece profile generated using the software according to the invention, but invoking a pierce function embodied in the software;
  • Figure 11 is a cross section through the x and z axes of an engraved workpiece showing part of the workpiece profile generated using the software according to the invention, but invoking a lift function and a negative function using the software;
  • Figure 12a is a flowchart showing the first part of the main program dmc_1000 for producing a two dimensional image from a scanned three dimensional relief of a stratum of material in accordance with an alternative method of the embodiment;
  • Figure 12b is a flowchart showing the second part of the main program dmc IOOO.
  • the embodiment is directed toward conversion software for converting a bitmap file ( * .bmp) to a file of a suitable format, and controlling hardware to cut and sculpt an image in 3 dimensions corresponding to the image in the input bitmap file.
  • the method of the embodiment transposes computer graphic images onto or into the surface of a material work piece via a computer numerically controlled tool.
  • the tool may be a material removal method or material deposition method or alteration of the material chemistry method, producing either a sculptured form or surface colouring via chemical alteration of the material.
  • the method of the embodiment may be used to record the sculptured form of a material subject as a computer graphic image, in this case the tool is a contact or non contact measuring device.
  • the recording of a sculptured form as a computer graphic image, and the production of a sculptured form therefrom, may be utilised to create a reproduction of an object.
  • the input computer graphic image may be in any format, but for convenience the software is designed to operate with a 24 bit bitmap ( * .bmp) file as the input file.
  • bitmap * .bmp
  • the bitmap file may have any origin, and may be derived from a colour photograph or a drawing.
  • the bitmap graphic file is edited and various functions performed upon it depending on the desired final machine controlled result required.
  • the graphics file may be edited by altering the colour or shade of the pixel that will correspond to the height or z axis of the matrix, and by increasing or decreasing the number of pixel's that construct the rows or columns of the matrix (y axis width and x axis length).
  • Software for performing such editing is readily available commercially.
  • the image is then converted into a monochrome image having 256 grey scale levels, with each level from 0 to 255 representing a depth being cut into a work piece.
  • the number of grey scale levels chosen is dependent upon the resolution required in the depth increments.
  • Each individual pixel in the edited bitmap file has a grey scale value which corresponds to a depth value in a work piece, at a position along the work piece which corresponds to the position of the pixel in the bitmap file.
  • the edited bitmap file is then translated into a three dimensional machine control operating code via translation software which is shown in figures 1 to 6.
  • bitmap may be colour
  • FIG. 1 the main part of the program is shown.
  • a graphical user interface should be utilised. The user would then be presented with a settings box in which the file to translate is entered. Once the "OK" button has been selected, the translation may begin. The program then performs the following:
  • the OpenFile subroutine 21 is called, and a file named alphabetl .dmc is opened.
  • the program then opens a dialog box 25 to allow the operator to select parameters for the resultant machine control code which will be stored in the target file alphabetl .dmc.
  • the following options are allowed:
  • the program calls the Translate subroutine which is shown in figures 2 to 6.
  • the translation software reads the edited bitmap file in raster, converting each - 11 - individual pixel described by bytes into the machine control code, which is stored together with header information in the alphabetl .dmc file.
  • the machine position instruction is prescribed by x and y co-ordinates depending upon the pixel location on the bitmap file matrix, and prescribed by a z co-ordinate representing depth of the tool depending upon the grey scale value for that pixel.
  • a sample profile is shown, showing variation in height of an engraving through an x axis.
  • the high points A represent white in the grey scale bitmap, while the lower points B represent darker shades.
  • the TranslatePass subroutine is then called, and translation is accomplished by loading one complete line of bits from a 2 bitmap, and this information is written in the machine control code. This procedure is performed iteratively, line by line, until all rows of bit map information have been converted into machine control code. At the end of each line of bit map information a indexing set of machine commands are written into the target file to index the machine to the beginning of the next line. During the translation of each line the user selected settings are taken into account.
  • the subroutine branches as shown in figure 3 in order to read pixels and convert into machine control code in a fashion to index the machine from one spiral or circular revolution to the next.
  • the tool will dwell in the selected position until 500 characters or less if so selected, have been sent to the machine buffer.
  • the figure of 500 characters is the number of characters that constitute a line, in the machine used by the inventor, and should be varied for different machines. This function ensures the machine has enough information so as not to be hindered in its execution of commands due to a lack of data.
  • the TranslatePass subroutine writes the first bit information from the bit map as the last instruction of machine code in the line of bit map translated information. In addition the TranslatePass subroutine decrements the bit map translated information position W for the value of the next position along the line. In the case of mirror image not being selected, the TranslatePass subroutine writes the first bit information from the bit map as the first instruction of machine code in the line of bit map translated information, and increments the bit map translated information position W for the value of the next position along the line.
  • Figure 8 shows a sample profile, showing variation in height of an engraving through an x axis. This cross section results from the same instructions utilised to produce the image shown in figure 7, except that the mirror image function has been invoked.
  • the mirror function may be used to perform a mirror image operation on a file about a central axis through the x or y axis plane. This enables a non symmetrical form to be sculpted on both sides of an object, and have the identical aspects of each point of the non symmetrical form directly opposite each other.
  • an image of a non symmetrical tree was to be sculpted into one side of a coin with holes cut through the material between the leaves and branches (using the pierce function), and the identical procedure was repeated on the other side of the coin with the mirror image, the holes between the leaves on both sides would directly line up as would the form of the branches.
  • the BmWrite subroutine performs an inversion by subtracting the actual colour value (a value between 0 and 255) from 255 for each pixel in each line, first for the blue values, then the green values, and then the red values. Once the values for red, blue and green have been determined for each pixel, the BmWrite subroutine performs a colour value check for each pixel, comparing the values for red blue and green, and alerts the operator that the bitmap may not be a grey scale bitmap if the values do not match.
  • Figure 9 shows a sample - 13 - profile, showing variation in height of an engraving through an x axis. This cross section results from the same instructions utilised to produce the image shown in figure 7, except that the negative image function has been invoked.
  • pierce function is selected in the settings dialog box 25 then set the z axis value for the position corresponding to the current pixel to the pierce depth value.
  • the pierce depth value should be set to a value which correlates to a depth in excess of the thickness of the material being worked, so that the tool pierces the material.
  • Figure 10 shows a cross section through the x axis of an engraving, using the same instructions utilised to produce the image shown in figure 7, but with the pierce function invoked, which has resulted in apertures C through the work.
  • the pierce depth value is set to a value which corresponds to an altitude above the engraving on the material a sculptured surface may be produced with columns of nominated height protruding therefrom, as shown in figure 11.
  • the skipover subroutine shown in figure 6 checks to see if three or more pixels in the same row have identical z values and if so the tool is indexed at the same z value from the first to the last pixel having the same value. This function reduces the amount of machine control code used if more than three pixels have the same value.
  • the quick traverse routine shown in figures 3 and 4 checks to determine if the colour value is pure white and if so machine control code is written to lift the tool the specified amount above the work and quick traverse to the next pixel that has a non pure white value in the same row, and lower the cutter the specified amount and commence operation.
  • an object recorder comprising scanning means to scan the three dimensional relief and provide elevation values in digital form to the data processing means.
  • the data processing means includes translation means to translate these elevation values to light values and these light values are sequentially stored as pixel data representing the two dimensional graphic representation of the three dimensional relief.
  • the machine includes a computer control system including software which operates the machine in accordance with the flowchart shown in figures 12a and 12b of the drawings.
  • the object recorder utilised for producing the two dimensional graphic representation or bitmap file may be a laser scanner, encoded stylus, video camera, digital camera or any other device used to record images from the real world or printed matter into a computer file, including any of the above mentioned numerically controlled machinery fitted with distance measuring apparatus or other special purpose machinery that guides a measurement recording tool over the object placing the data into a computer file.
  • the invention may be utilised to produce inter alia sculptured surfaces in or on a material surface, in any relief as desired.
  • Such sculptured surfaces may be produced on any - 17/3 - desired back plane, including fiat back planes or back planes having a circular periphery about a central axis.
  • Envisaged applications include any application where a sunk or raised bar relief form is required, and include the production of moulds for plastic injection, lost wax, and tool production for hobbing, and forming blanking press tools. It will be clear that methods such as electro discharge erosion machining, commonly utilised in tool production, may be utilised.
  • Direct application may be made of the invention for jewellery manufacture, coin or medallion carving, and sculptures, mould and die manufacture, toolage etc.
  • the invention may be utilised for recording the form of an object, whether the object is fully three dimensional or a sculptural form, in high or low relief, or whether the back plane of the object is flat or cylindrical. Once the form of the object has been recorded in this manner, the object may be reproduced at any scale and in any chosen material.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Manufacture Or Reproduction Of Printing Formes (AREA)

Abstract

Procédé et dispositif permettant d'effectuer, à partir d'une image bidimensionnelle, une conversion entre cette image et un relief tridimensionnel ou un traitement de surface de matériau d'une couche de matériau, afin de produire respectivement une surface tridimensionnelle ou une surface traitée. On décrit également un procédé ainsi qu'un dispositif de reproduction d'un relief tridimensionnel ou d'un traitement de surface de matériau par production d'une image bidimensionnelle à partir d'un relief tridimensionnel. Ce dispositif comprend des moyens de traitement de données pourvus d'une interface avec un dispositif de traitement de matériau, ainsi que des moyens destinés à effectuer une translation entre une image comprenant un faisceau bidimensionnel de pixels et un relief tridimensionnel ou traitement de surface de matériau. Ces moyens de translation sont conçus pour effectuer une translation de valeur d'élévation ou de profondeur, en un certain emplacement dans ou sur la couche de matériau, en réponse à une valeur lumineuse pour un pixel en un emplacement correspondant dans ladite image, ou proportionnellement à cette valeur lumineuse.
PCT/AU1996/000139 1995-03-13 1996-03-13 Procede et systeme de translation entre une image et un relief tridimensionnel WO1996028927A1 (fr)

Priority Applications (1)

Application Number Priority Date Filing Date Title
AU48716/96A AU4871696A (en) 1995-03-13 1996-03-13 Method and system for translating between an image and a 3-dimensional relief

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
AUPN1697 1995-03-13
AUPN1697A AUPN169795A0 (en) 1995-03-13 1995-03-13 Method and system for transforming a computer graphic file

Publications (1)

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WO1996028927A1 true WO1996028927A1 (fr) 1996-09-19

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WO (1) WO1996028927A1 (fr)
ZA (1) ZA962022B (fr)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10109880A1 (de) * 2001-02-27 2002-09-05 4D Vision Gmbh Verfahren und Vorrichtung zur Erstellung einer Tiefenkarte zu einem zweidimensionalen Bild und zur Übertragung von räumlichen Bildinformationen
WO2004069508A2 (fr) * 2003-02-04 2004-08-19 Fintrade S.R.L Systeme permettant de thermoformer, de numeriser et de reproduire la surface externe d'un objet en trois dimensions, sous forme virtuelle et/ou en matiere plastique thermoformable
JP2021081390A (ja) * 2019-11-22 2021-05-27 株式会社指月電機製作所 版の検査方法及び版の検査装置
CN113732539A (zh) * 2021-09-10 2021-12-03 淮阴工学院 一种激光雕刻打孔调节机构及其使用方法

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US4385360A (en) * 1980-08-04 1983-05-24 Micro-Power Computer Systems Computer-controlled reproduction device
WO1983004114A1 (fr) * 1982-05-18 1983-11-24 Gareth David Thomas Procede et appareil permettant d'effectuer des operations sur des surfaces tridimensionnelles
EP0257965A2 (fr) * 1986-08-18 1988-03-02 Fazlollah Samangooie Fabrication de maquettes
EP0328443A1 (fr) * 1988-02-09 1989-08-16 Sa Kreon Industrie Procédé de numérisation de la surface d'un objet tridimensionnel et appareil de relevé en vue de sa mise en oeuvre
WO1989009378A1 (fr) * 1988-03-25 1989-10-05 Kreon Procede de determination et de reconstitution des coordonnees spatiales de chacun des points d'un ensemble de points echantillonnant une surface tridimensionnelle, et procede de realisation d'une image tridimensionnelle de cette surface a partir desdites coordonnees
EP0365001A2 (fr) * 1988-10-20 1990-04-25 Yoichi Madokoro Méthode et dispositif d'usinage en trois dimensions
EP0380432A2 (fr) * 1989-01-23 1990-08-01 Vision Numeric Procédé et dispositif de réalisation d'un objet à partir d'une saisie tridimensionnelle de formes
EP0398352A2 (fr) * 1989-05-19 1990-11-22 Petio Co., Ltd. Un système automatique de gravure
EP0433013A2 (fr) * 1989-12-15 1991-06-19 Sony Corporation Méthode pour introduire des données de configuration tridimensionnelles
US5173947A (en) * 1989-08-01 1992-12-22 Martin Marietta Corporation Conformal image processing apparatus and method

Patent Citations (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4385360A (en) * 1980-08-04 1983-05-24 Micro-Power Computer Systems Computer-controlled reproduction device
WO1983004114A1 (fr) * 1982-05-18 1983-11-24 Gareth David Thomas Procede et appareil permettant d'effectuer des operations sur des surfaces tridimensionnelles
EP0257965A2 (fr) * 1986-08-18 1988-03-02 Fazlollah Samangooie Fabrication de maquettes
EP0328443A1 (fr) * 1988-02-09 1989-08-16 Sa Kreon Industrie Procédé de numérisation de la surface d'un objet tridimensionnel et appareil de relevé en vue de sa mise en oeuvre
WO1989009378A1 (fr) * 1988-03-25 1989-10-05 Kreon Procede de determination et de reconstitution des coordonnees spatiales de chacun des points d'un ensemble de points echantillonnant une surface tridimensionnelle, et procede de realisation d'une image tridimensionnelle de cette surface a partir desdites coordonnees
EP0365001A2 (fr) * 1988-10-20 1990-04-25 Yoichi Madokoro Méthode et dispositif d'usinage en trois dimensions
EP0380432A2 (fr) * 1989-01-23 1990-08-01 Vision Numeric Procédé et dispositif de réalisation d'un objet à partir d'une saisie tridimensionnelle de formes
EP0398352A2 (fr) * 1989-05-19 1990-11-22 Petio Co., Ltd. Un système automatique de gravure
US5173947A (en) * 1989-08-01 1992-12-22 Martin Marietta Corporation Conformal image processing apparatus and method
EP0433013A2 (fr) * 1989-12-15 1991-06-19 Sony Corporation Méthode pour introduire des données de configuration tridimensionnelles

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10109880A1 (de) * 2001-02-27 2002-09-05 4D Vision Gmbh Verfahren und Vorrichtung zur Erstellung einer Tiefenkarte zu einem zweidimensionalen Bild und zur Übertragung von räumlichen Bildinformationen
WO2004069508A2 (fr) * 2003-02-04 2004-08-19 Fintrade S.R.L Systeme permettant de thermoformer, de numeriser et de reproduire la surface externe d'un objet en trois dimensions, sous forme virtuelle et/ou en matiere plastique thermoformable
WO2004069508A3 (fr) * 2003-02-04 2005-07-07 Fintrade S R L Systeme permettant de thermoformer, de numeriser et de reproduire la surface externe d'un objet en trois dimensions, sous forme virtuelle et/ou en matiere plastique thermoformable
JP2021081390A (ja) * 2019-11-22 2021-05-27 株式会社指月電機製作所 版の検査方法及び版の検査装置
CN113732539A (zh) * 2021-09-10 2021-12-03 淮阴工学院 一种激光雕刻打孔调节机构及其使用方法

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AUPN169795A0 (en) 1995-04-06
ZA962022B (en) 1997-10-13

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