{"id":10521,"date":"2022-09-24T00:12:13","date_gmt":"2022-09-23T18:42:13","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-triangular-pyramid-trigonal-pyramid-offset-3d-plane-intersection-by-vbasolver\/"},"modified":"2022-09-24T00:12:13","modified_gmt":"2022-09-23T18:42:13","slug":"solved-triangular-pyramid-trigonal-pyramid-offset-3d-plane-intersection-by-vbasolver","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-triangular-pyramid-trigonal-pyramid-offset-3d-plane-intersection-by-vbasolver\/","title":{"rendered":"[Solved] triangular pyramid, trigonal pyramid offset-3d-Plane-Intersection By vbasolver"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-69983868\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"69983868\" data-parentid=\"69616176\" data-score=\"0\" data-position-on-page=\"1\" data-highest-scored=\"1\" data-question-has-accepted-highest-score=\"1\" itemprop=\"acceptedAnswer\" itemscope itemtype=\"https:\/\/schema.org\/Answer\">\n<div class=\"post-layout\">\n<div class=\"votecell post-layout--left\"><\/div>\n<div class=\"answercell post-layout--right\">\n<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>I check<\/p>\n<pre><code>from sympy import *\nvar('m')\ndef myUnitVector(myPoint3D):\n    myL=myPoint3D.distance((0, 0))\n    return Point3D(myPoint3D.x\/myL,myPoint3D.y\/myL,myPoint3D.z\/myL)\ndef myHtoP(myHairetu):\n    return Point3D(myHairetu[0],myHairetu[1],myHairetu[2])\ndef my3PLaneIntersection(PTO,PTA,PTB,PTC,RA,RB,RC):\n    vA =myUnitVector(myHtoP(Plane(PTO, PTB, PTC).normal_vector))\n    PLA=Plane(PTO + RA * vA, normal_vector=vA)\n    vB =myUnitVector(myHtoP(Plane(PTO, PTC, PTA).normal_vector))\n    PLB=Plane(PTO + RB * vB, normal_vector=vB)\n    vC =myUnitVector(myHtoP(Plane(PTO, PTA, PTB).normal_vector))\n    PLC=Plane(PTO + RC * vC, normal_vector=vC)\n    return PLC.intersection(PLB.intersection(PLA)[0])\ndef myProjection(PTO,PTA,PTC,PTOO):\n    v = myUnitVector(myHtoP(Plane(PTO, PTA, PTC).normal_vector))\n    return solve(PTOO - Plane(PTO, PTA, PTC).projection(PTOO) - m * v, m)[m] * (-1)\nPTO,PTA,PTB,PTC=Point3D(0,0,0),Point3D(1,0,0),Point3D(0,1,0),Point3D(0,0,2)\nmyRO,myRA,myRB,myRC=-1\/4,-1\/4,-1\/4,-1\/4\nPTOO= my3PLaneIntersection(PTO, PTA,PTB,PTC,myRO,myRO,myRO)[0]\nPTAA= my3PLaneIntersection(PTA, PTC,PTB,PTO,myRA,myRA,myRA)[0]\nPTBB= my3PLaneIntersection(PTB, PTC,PTO,PTA,myRB,myRB,myRB)[0]\nPTCC= my3PLaneIntersection(PTC, PTB,PTA,PTO,myRC,myRC,myRC)[0]\nprint(\"#\",PTOO,\"\\n#\",PTAA,\"\\n#\",PTBB,\"\\n#\",PTCC,)\nprint(\"#\",myProjection(PTO,PTB,PTA,PTOO),\n          myProjection(PTO,PTA,PTC,PTOO),\n          myProjection(PTO,PTC,PTB,PTOO))\nprint(\"#\",myProjection(PTA,PTO,PTB,PTAA),\n          myProjection(PTA,PTC,PTO,PTAA),\n          myProjection(PTA,PTB,PTC,PTAA))\nprint(\"#\",myProjection(PTB,PTA,PTO,PTBB),\n          myProjection(PTB,PTO,PTC,PTBB),\n          myProjection(PTB,PTC,PTA,PTBB))\nprint(\"#\",myProjection(PTC,PTO,PTA,PTCC),\n          myProjection(PTC,PTB,PTO,PTCC),\n          myProjection(PTC,PTA,PTB,PTCC))\n# Point3D(-1\/4, -1\/4, -1\/4) \n# Point3D(7\/4, -1\/4, -1\/4) \n# Point3D(-1\/4, 7\/4, -1\/4) \n# Point3D(-1\/4, -1\/4, 15\/4)\n# -1\/4 -1\/4 -1\/4\n# -1\/4 -1\/4 -1\/4\n# -1\/4 -1\/4 -1\/4\n# -1\/4 -1\/4 -1\/4\n<\/code><\/pre>\n<\/p><\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\">1<\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved triangular pyramid, trigonal pyramid offset-3d-Plane-Intersection By vbasolver <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] I check from sympy import * var(&#8216;m&#8217;) def myUnitVector(myPoint3D): myL=myPoint3D.distance((0, 0)) return Point3D(myPoint3D.x\/myL,myPoint3D.y\/myL,myPoint3D.z\/myL) def myHtoP(myHairetu): return Point3D(myHairetu[0],myHairetu[1],myHairetu[2]) def my3PLaneIntersection(PTO,PTA,PTB,PTC,RA,RB,RC): vA =myUnitVector(myHtoP(Plane(PTO, PTB, PTC).normal_vector)) PLA=Plane(PTO + RA * vA, normal_vector=vA) vB =myUnitVector(myHtoP(Plane(PTO, PTC, PTA).normal_vector)) PLB=Plane(PTO + RB * vB, normal_vector=vB) vC =myUnitVector(myHtoP(Plane(PTO, PTA, PTB).normal_vector)) PLC=Plane(PTO + RC * vC, normal_vector=vC) return PLC.intersection(PLB.intersection(PLA)[0]) def myProjection(PTO,PTA,PTC,PTOO): v &#8230; <a title=\"[Solved] triangular pyramid, trigonal pyramid offset-3d-Plane-Intersection By vbasolver\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-triangular-pyramid-trigonal-pyramid-offset-3d-plane-intersection-by-vbasolver\/\" aria-label=\"More on [Solved] triangular pyramid, trigonal pyramid offset-3d-Plane-Intersection By vbasolver\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[2897,2898,2896,401],"class_list":["post-10521","post","type-post","status-publish","format-standard","hentry","category-solved","tag-offset","tag-solver","tag-sympy","tag-vba"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>[Solved] triangular pyramid, trigonal pyramid offset-3d-Plane-Intersection By vbasolver - JassWeb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jassweb.com\/solved\/solved-triangular-pyramid-trigonal-pyramid-offset-3d-plane-intersection-by-vbasolver\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] triangular pyramid, trigonal pyramid offset-3d-Plane-Intersection By vbasolver - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] I check from sympy import * var(&#039;m&#039;) def myUnitVector(myPoint3D): myL=myPoint3D.distance((0, 0)) return Point3D(myPoint3D.x\/myL,myPoint3D.y\/myL,myPoint3D.z\/myL) def myHtoP(myHairetu): return Point3D(myHairetu[0],myHairetu[1],myHairetu[2]) def my3PLaneIntersection(PTO,PTA,PTB,PTC,RA,RB,RC): vA =myUnitVector(myHtoP(Plane(PTO, PTB, PTC).normal_vector)) PLA=Plane(PTO + RA * vA, normal_vector=vA) vB =myUnitVector(myHtoP(Plane(PTO, PTC, PTA).normal_vector)) PLB=Plane(PTO + RB * vB, normal_vector=vB) vC =myUnitVector(myHtoP(Plane(PTO, PTA, PTB).normal_vector)) PLC=Plane(PTO + RC * vC, normal_vector=vC) return PLC.intersection(PLB.intersection(PLA)[0]) def myProjection(PTO,PTA,PTC,PTOO): v ... 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JassWeb","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/jassweb.com\/solved\/solved-triangular-pyramid-trigonal-pyramid-offset-3d-plane-intersection-by-vbasolver\/","og_locale":"en_US","og_type":"article","og_title":"[Solved] triangular pyramid, trigonal pyramid offset-3d-Plane-Intersection By vbasolver - JassWeb","og_description":"[ad_1] I check from sympy import * var('m') def myUnitVector(myPoint3D): myL=myPoint3D.distance((0, 0)) return Point3D(myPoint3D.x\/myL,myPoint3D.y\/myL,myPoint3D.z\/myL) def myHtoP(myHairetu): return Point3D(myHairetu[0],myHairetu[1],myHairetu[2]) def my3PLaneIntersection(PTO,PTA,PTB,PTC,RA,RB,RC): vA =myUnitVector(myHtoP(Plane(PTO, PTB, PTC).normal_vector)) PLA=Plane(PTO + RA * vA, normal_vector=vA) vB =myUnitVector(myHtoP(Plane(PTO, PTC, PTA).normal_vector)) PLB=Plane(PTO + RB * vB, normal_vector=vB) vC =myUnitVector(myHtoP(Plane(PTO, PTA, PTB).normal_vector)) PLC=Plane(PTO + RC * vC, normal_vector=vC) return PLC.intersection(PLB.intersection(PLA)[0]) def myProjection(PTO,PTA,PTC,PTOO): v ... 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