The Monge theorem and its application in engineering practice
Abstract Engineering innovation activities cannot be performed without mathematical devices. The present paper describes the theoretical analysis of the reconstruction of the Monge theorem. The significance of the analysis is that we consider those Monge projections the same, which can be translated...
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| Autor*in: |
Balajti, Zsuzsanna [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag London 2016 |
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| Übergeordnetes Werk: |
Enthalten in: The international journal of advanced manufacturing technology - London : Springer, 1985, 91(2016), 1-4 vom: 28. Nov., Seite 739-749 |
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| Übergeordnetes Werk: |
volume:91 ; year:2016 ; number:1-4 ; day:28 ; month:11 ; pages:739-749 |
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| DOI / URN: |
10.1007/s00170-016-9763-1 |
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SPR001449796 |
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| 520 | |a Abstract Engineering innovation activities cannot be performed without mathematical devices. The present paper describes the theoretical analysis of the reconstruction of the Monge theorem. The significance of the analysis is that we consider those Monge projections the same, which can be translated to one another by parallel shifting. Accordingly, in a fixed Descartes coordinate system in the space, every Monge projection is determined by its two projection lines that go through the origin point, which is described by three free parameters. The three free parameters determining the Monge projections make up the points of the Monge cuboid. We are looking for Monge projections to a fixed third-grade spatial curve, in which the reconstruction of the curve can be carried out only with two pictures without any further information. The inner points of the Monge cuboid—defined by the bijective Monge projections—are bordered by a surface. This surface is described in this article during our research work first. We have proved the engineering application of this theorem by calculating the correct camera position for the wearing examination of the hob’s cutting edge. | ||
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10.1007/s00170-016-9763-1 doi (DE-627)SPR001449796 (SPR)s00170-016-9763-1-e DE-627 ger DE-627 rakwb eng Balajti, Zsuzsanna verfasserin aut The Monge theorem and its application in engineering practice 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag London 2016 Abstract Engineering innovation activities cannot be performed without mathematical devices. The present paper describes the theoretical analysis of the reconstruction of the Monge theorem. The significance of the analysis is that we consider those Monge projections the same, which can be translated to one another by parallel shifting. Accordingly, in a fixed Descartes coordinate system in the space, every Monge projection is determined by its two projection lines that go through the origin point, which is described by three free parameters. The three free parameters determining the Monge projections make up the points of the Monge cuboid. We are looking for Monge projections to a fixed third-grade spatial curve, in which the reconstruction of the curve can be carried out only with two pictures without any further information. The inner points of the Monge cuboid—defined by the bijective Monge projections—are bordered by a surface. This surface is described in this article during our research work first. We have proved the engineering application of this theorem by calculating the correct camera position for the wearing examination of the hob’s cutting edge. Monge (dpeaa)DE-He213 Worm gear (dpeaa)DE-He213 Hob (dpeaa)DE-He213 Projection (dpeaa)DE-He213 Dudás, Illés aut Enthalten in The international journal of advanced manufacturing technology London : Springer, 1985 91(2016), 1-4 vom: 28. Nov., Seite 739-749 (DE-627)270127712 (DE-600)1476510-X 1433-3015 nnns volume:91 year:2016 number:1-4 day:28 month:11 pages:739-749 https://dx.doi.org/10.1007/s00170-016-9763-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 91 2016 1-4 28 11 739-749 |
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10.1007/s00170-016-9763-1 doi (DE-627)SPR001449796 (SPR)s00170-016-9763-1-e DE-627 ger DE-627 rakwb eng Balajti, Zsuzsanna verfasserin aut The Monge theorem and its application in engineering practice 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag London 2016 Abstract Engineering innovation activities cannot be performed without mathematical devices. The present paper describes the theoretical analysis of the reconstruction of the Monge theorem. The significance of the analysis is that we consider those Monge projections the same, which can be translated to one another by parallel shifting. Accordingly, in a fixed Descartes coordinate system in the space, every Monge projection is determined by its two projection lines that go through the origin point, which is described by three free parameters. The three free parameters determining the Monge projections make up the points of the Monge cuboid. We are looking for Monge projections to a fixed third-grade spatial curve, in which the reconstruction of the curve can be carried out only with two pictures without any further information. The inner points of the Monge cuboid—defined by the bijective Monge projections—are bordered by a surface. This surface is described in this article during our research work first. We have proved the engineering application of this theorem by calculating the correct camera position for the wearing examination of the hob’s cutting edge. Monge (dpeaa)DE-He213 Worm gear (dpeaa)DE-He213 Hob (dpeaa)DE-He213 Projection (dpeaa)DE-He213 Dudás, Illés aut Enthalten in The international journal of advanced manufacturing technology London : Springer, 1985 91(2016), 1-4 vom: 28. Nov., Seite 739-749 (DE-627)270127712 (DE-600)1476510-X 1433-3015 nnns volume:91 year:2016 number:1-4 day:28 month:11 pages:739-749 https://dx.doi.org/10.1007/s00170-016-9763-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 91 2016 1-4 28 11 739-749 |
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10.1007/s00170-016-9763-1 doi (DE-627)SPR001449796 (SPR)s00170-016-9763-1-e DE-627 ger DE-627 rakwb eng Balajti, Zsuzsanna verfasserin aut The Monge theorem and its application in engineering practice 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag London 2016 Abstract Engineering innovation activities cannot be performed without mathematical devices. The present paper describes the theoretical analysis of the reconstruction of the Monge theorem. The significance of the analysis is that we consider those Monge projections the same, which can be translated to one another by parallel shifting. Accordingly, in a fixed Descartes coordinate system in the space, every Monge projection is determined by its two projection lines that go through the origin point, which is described by three free parameters. The three free parameters determining the Monge projections make up the points of the Monge cuboid. We are looking for Monge projections to a fixed third-grade spatial curve, in which the reconstruction of the curve can be carried out only with two pictures without any further information. The inner points of the Monge cuboid—defined by the bijective Monge projections—are bordered by a surface. This surface is described in this article during our research work first. We have proved the engineering application of this theorem by calculating the correct camera position for the wearing examination of the hob’s cutting edge. Monge (dpeaa)DE-He213 Worm gear (dpeaa)DE-He213 Hob (dpeaa)DE-He213 Projection (dpeaa)DE-He213 Dudás, Illés aut Enthalten in The international journal of advanced manufacturing technology London : Springer, 1985 91(2016), 1-4 vom: 28. Nov., Seite 739-749 (DE-627)270127712 (DE-600)1476510-X 1433-3015 nnns volume:91 year:2016 number:1-4 day:28 month:11 pages:739-749 https://dx.doi.org/10.1007/s00170-016-9763-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 91 2016 1-4 28 11 739-749 |
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10.1007/s00170-016-9763-1 doi (DE-627)SPR001449796 (SPR)s00170-016-9763-1-e DE-627 ger DE-627 rakwb eng Balajti, Zsuzsanna verfasserin aut The Monge theorem and its application in engineering practice 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag London 2016 Abstract Engineering innovation activities cannot be performed without mathematical devices. The present paper describes the theoretical analysis of the reconstruction of the Monge theorem. The significance of the analysis is that we consider those Monge projections the same, which can be translated to one another by parallel shifting. Accordingly, in a fixed Descartes coordinate system in the space, every Monge projection is determined by its two projection lines that go through the origin point, which is described by three free parameters. The three free parameters determining the Monge projections make up the points of the Monge cuboid. We are looking for Monge projections to a fixed third-grade spatial curve, in which the reconstruction of the curve can be carried out only with two pictures without any further information. The inner points of the Monge cuboid—defined by the bijective Monge projections—are bordered by a surface. This surface is described in this article during our research work first. We have proved the engineering application of this theorem by calculating the correct camera position for the wearing examination of the hob’s cutting edge. Monge (dpeaa)DE-He213 Worm gear (dpeaa)DE-He213 Hob (dpeaa)DE-He213 Projection (dpeaa)DE-He213 Dudás, Illés aut Enthalten in The international journal of advanced manufacturing technology London : Springer, 1985 91(2016), 1-4 vom: 28. Nov., Seite 739-749 (DE-627)270127712 (DE-600)1476510-X 1433-3015 nnns volume:91 year:2016 number:1-4 day:28 month:11 pages:739-749 https://dx.doi.org/10.1007/s00170-016-9763-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 91 2016 1-4 28 11 739-749 |
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monge theorem and its application in engineering practice |
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The Monge theorem and its application in engineering practice |
| abstract |
Abstract Engineering innovation activities cannot be performed without mathematical devices. The present paper describes the theoretical analysis of the reconstruction of the Monge theorem. The significance of the analysis is that we consider those Monge projections the same, which can be translated to one another by parallel shifting. Accordingly, in a fixed Descartes coordinate system in the space, every Monge projection is determined by its two projection lines that go through the origin point, which is described by three free parameters. The three free parameters determining the Monge projections make up the points of the Monge cuboid. We are looking for Monge projections to a fixed third-grade spatial curve, in which the reconstruction of the curve can be carried out only with two pictures without any further information. The inner points of the Monge cuboid—defined by the bijective Monge projections—are bordered by a surface. This surface is described in this article during our research work first. We have proved the engineering application of this theorem by calculating the correct camera position for the wearing examination of the hob’s cutting edge. © Springer-Verlag London 2016 |
| abstractGer |
Abstract Engineering innovation activities cannot be performed without mathematical devices. The present paper describes the theoretical analysis of the reconstruction of the Monge theorem. The significance of the analysis is that we consider those Monge projections the same, which can be translated to one another by parallel shifting. Accordingly, in a fixed Descartes coordinate system in the space, every Monge projection is determined by its two projection lines that go through the origin point, which is described by three free parameters. The three free parameters determining the Monge projections make up the points of the Monge cuboid. We are looking for Monge projections to a fixed third-grade spatial curve, in which the reconstruction of the curve can be carried out only with two pictures without any further information. The inner points of the Monge cuboid—defined by the bijective Monge projections—are bordered by a surface. This surface is described in this article during our research work first. We have proved the engineering application of this theorem by calculating the correct camera position for the wearing examination of the hob’s cutting edge. © Springer-Verlag London 2016 |
| abstract_unstemmed |
Abstract Engineering innovation activities cannot be performed without mathematical devices. The present paper describes the theoretical analysis of the reconstruction of the Monge theorem. The significance of the analysis is that we consider those Monge projections the same, which can be translated to one another by parallel shifting. Accordingly, in a fixed Descartes coordinate system in the space, every Monge projection is determined by its two projection lines that go through the origin point, which is described by three free parameters. The three free parameters determining the Monge projections make up the points of the Monge cuboid. We are looking for Monge projections to a fixed third-grade spatial curve, in which the reconstruction of the curve can be carried out only with two pictures without any further information. The inner points of the Monge cuboid—defined by the bijective Monge projections—are bordered by a surface. This surface is described in this article during our research work first. We have proved the engineering application of this theorem by calculating the correct camera position for the wearing examination of the hob’s cutting edge. © Springer-Verlag London 2016 |
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The Monge theorem and its application in engineering practice |
| url |
https://dx.doi.org/10.1007/s00170-016-9763-1 |
| remote_bool |
true |
| author2 |
Dudás, Illés |
| author2Str |
Dudás, Illés |
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270127712 |
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c |
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| doi_str |
10.1007/s00170-016-9763-1 |
| up_date |
2024-07-03T22:40:21.626Z |
| _version_ |
1803599396603953152 |
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The present paper describes the theoretical analysis of the reconstruction of the Monge theorem. The significance of the analysis is that we consider those Monge projections the same, which can be translated to one another by parallel shifting. Accordingly, in a fixed Descartes coordinate system in the space, every Monge projection is determined by its two projection lines that go through the origin point, which is described by three free parameters. The three free parameters determining the Monge projections make up the points of the Monge cuboid. We are looking for Monge projections to a fixed third-grade spatial curve, in which the reconstruction of the curve can be carried out only with two pictures without any further information. The inner points of the Monge cuboid—defined by the bijective Monge projections—are bordered by a surface. This surface is described in this article during our research work first. 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