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Question: is it possible to trim the surface along the intersection line in Maple?

Question:is it possible to trim the surface along the intersection line in Maple?

Tatyana 10 Maple
surface intersection plane plotting
June 28 2018
0
Hello!
I'm a beginner in Maple. My question is: is it possible to trim the surface along the intersection line in Maple? There is a problem - inclined surfaces are constructed along the contour of the triangle, they intersect. Is it possible to get a pyramid along the intersection lines?
Thank you!trimming_surfaces.mwtrimming_surfaces.mw
 

NULL

> 

restart; with(plots), with(plottools); with(linalg)
> 

Q1p := 45; Q1po := 75
> 

Q2p := 110; Q2po := 84
> 

Q3p := 63; Q3po := 120
> 

NULL
> 

NULL
> 

NULL
> 

XP := KTX1+(KTX2-KTX1)*t1
> 

YP := KTY1+(KTY2-KTY1)*t1
> 

NULL
> 

NULL
> 

x1 := subs({KTX1 = Q1p, KTX2 = Q2p, t1 = t1}, XP)
> 

y1 := subs({KTY1 = Q1po, KTY2 = Q2po, t1 = t1}, YP)
> 

NULL
> 

x2 := subs({KTX1 = Q2p, KTX2 = Q3p, t1 = t2}, XP)
> 

y2 := subs({KTY1 = Q2po, KTY2 = Q3po, t1 = t2}, YP)
> 

``

NULL

> 

x3 := subs({KTX1 = Q3p, KTX2 = Q1p, t1 = t3}, XP)
> 

y3 := subs({KTY1 = Q3po, KTY2 = Q1po, t1 = t3}, YP)
> 

NULL
> 

za := 0
> 

``
> 

Kriv1 := spacecurve([x1, y1, za, t1 = 0 .. 1], color = brown, scaling = constrained, thickness = 4)
> 

Kriv2 := spacecurve([x2, y2, za, t2 = 0 .. 1], color = green, scaling = constrained, thickness = 4)
> 

Kriv3 := spacecurve([x3, y3, za, t3 = 0 .. 1], color = blue, scaling = constrained, thickness = 4)
> 

NULL
> 

display(Kriv1, Kriv2, Kriv3)
> 

NULL
> 

NULL
> 

xE1 := x1-30*(diff(y1, t1))/sqrt((diff(x1, t1))^2+(diff(y1, t1))^2)
> 

yE1 := y1+30*(diff(x1, t1))/sqrt((diff(x1, t1))^2+(diff(y1, t1))^2)
> 

zE1 := 30
> 

KrivE1 := spacecurve([xE1, yE1, zE1, t1 = 0 .. 1], color = blue, scaling = constrained, thickness = 4)
> 

NULL
> 

xP1 := simplify(xE1+l1*(x1-xE1))
> 

yP1 := simplify(yE1+l1*(y1-yE1))
> 

zP1 := simplify(zE1*(1-l1))
> 

P1 := plot3d([xP1, yP1, zP1], t1 = 0 .. 1, l1 = 0 .. 1, transparency = 0)
> 

display(KrivE1, Kriv1, P1, Kriv2, Kriv3)

``

> 

NULL
> 

xE2 := x2-30*(diff(y2, t2))/sqrt((diff(x2, t2))^2+(diff(y2, t2))^2)
> 

yE2 := y2+30*(diff(x2, t2))/sqrt((diff(x2, t2))^2+(diff(y2, t2))^2)
> 

zE2 := 30
> 

KrivE2 := spacecurve([xE2, yE2, zE2, t2 = 0 .. 1], color = blue, scaling = constrained, thickness = 4)
> 

NULL
> 

xP2 := simplify(xE2+l2*(x2-xE2))
> 

yP2 := simplify(yE2+l2*(y2-yE2))
> 

zP2 := simplify(zE2*(1-l2))
> 

P2 := plot3d([xP2, yP2, zP2], t2 = 0 .. 1, l2 = 0 .. 1, transparency = 0)
> 

display(KrivE2, Kriv2, P2)
> 

NULL

NULL

> 

NULL
> 

xE3 := x3-30*(diff(y3, t3))/sqrt((diff(x3, t3))^2+(diff(y3, t3))^2)
> 

yE3 := y3+30*(diff(x3, t3))/sqrt((diff(x3, t3))^2+(diff(y3, t3))^2)
> 

zE3 := 30
> 

KrivE3 := spacecurve([xE3, yE3, zE3, t3 = 0 .. 1], color = blue, scaling = constrained, thickness = 4)
> 

NULL
> 

xP3 := simplify(xE3+l3*(x3-xE3))
> 

yP3 := simplify(yE3+l3*(y3-yE3))
> 

zP3 := simplify(zE3*(1-l3))
> 

P3 := plot3d([xP3, yP3, zP3], t3 = 0 .. 1, l3 = 0 .. 1, transparency = 0)
> 

display(KrivE3, Kriv3, P3)
> 

NULL

NULL

> 

NULL
> 

L22 := solve(zP2 = zP1, l2)
> 

L111 := solve(subs(l2 = L22, yP2 = yP1), l1)
> 

L222 := subs(l1 = L111, L22)
> 

T11 := solve(subs(l2 = L222, l1 = L111, xP2 = xP1), t1)
> 

L2T := subs(t1 = T11, L222)
> 

L1T := subs(t1 = T11, L111)
> 

LP12 := spacecurve([XT12, YT12, ZT12, t2 = 0 .. 1], color = red, scaling = constrained, thickness = 1)

PLOT3D(CURVES([[110., 84., 0.], [108.7339864, 84.33411040, .5045906412], [107.4679728, 84.66822079, 1.009181282], [106.2019593, 85.00233119, 1.513771924], [104.9359457, 85.33644158, 2.018362565], [103.6699321, 85.67055198, 2.522953207], [102.4039185, 86.00466237, 3.027543849], [101.1379050, 86.33877277, 3.532134491], [99.87189139, 86.67288316, 4.036725133], [98.60587781, 87.00699356, 4.541315775], [97.33986423, 87.34110395, 5.045906417], [96.07385066, 87.67521435, 5.550497059], [94.80783708, 88.00932474, 6.055087701], [93.54182350, 88.34343514, 6.559678343], [92.27580993, 88.67754554, 7.064268985], [91.00979635, 89.01165593, 7.568859626], [89.74378277, 89.34576633, 8.073450268], [88.47776919, 89.67987672, 8.578040910], [87.21175562, 90.01398712, 9.082631552], [85.94574204, 90.34809751, 9.587222194], [84.67972846, 90.68220791, 10.09181284], [83.41371488, 91.01631830, 10.59640348], [82.14770131, 91.35042870, 11.10099412], [80.88168773, 91.68453909, 11.60558476], [79.61567415, 92.01864949, 12.11017540], [78.34966058, 92.35275989, 12.61476605], [77.08364700, 92.68687028, 13.11935669], [75.81763342, 93.02098068, 13.62394733], [74.55161984, 93.35509107, 14.12853797], [73.28560627, 93.68920147, 14.63312861], [72.01959269, 94.02331186, 15.13771926], [70.75357911, 94.35742226, 15.64230990], [69.48756554, 94.69153265, 16.14690054], [68.22155196, 95.02564305, 16.65149118], [66.95553838, 95.35975345, 17.15608182], [65.68952480, 95.69386384, 17.66067247], [64.42351123, 96.02797424, 18.16526311], [63.15749765, 96.36208463, 18.66985375], [61.89148407, 96.69619503, 19.17444439], [60.62547050, 97.03030542, 19.67903503], [59.35945692, 97.36441582, 20.18362567], [58.09344334, 97.69852621, 20.68821632], [56.82742976, 98.03263661, 21.19280696], [55.56141619, 98.36674700, 21.69739760], [54.29540261, 98.70085740, 22.20198824], [53.02938903, 99.03496780, 22.70657888], [51.76337545, 99.36907819, 23.21116953], [50.49736188, 99.70318859, 23.71576017], [49.23134830, 100.0372990, 24.22035081], [47.96533470, 100.3714094, 24.72494146]], COLOUR(RGB, 1.00000000, 0., 0.)), THICKNESS(1), SCALING(CONSTRAINED))

 (1)

``

> 

NULL
> 

NULL``
> 

L22 := solve(zP2 = zP3, l2)
> 

L333 := solve(subs(l2 = L22, yP2 = yP3), l3)
> 

L222 := subs(l3 = L333, L22)
> 

T33 := solve(subs(l2 = L222, l3 = L333, xP2 = xP3), t3)
> 

L2T := subs(t3 = T33, L222)
> 

L3T := subs(t3 = T33, L333)
> 

LP32 := spacecurve([XT32, YT32, ZT32, t2 = 0 .. 1], color = red, scaling = constrained, thickness = 3)

PLOT3D(CURVES([[82.69885121, 48.35683352, 44.89752824], [82.29683384, 49.81893896, 43.98125215], [81.89481646, 51.28104440, 43.06497607], [81.49279909, 52.74314984, 42.14869998], [81.09078172, 54.20525528, 41.23242389], [80.68876435, 55.66736072, 40.31614780], [80.28674698, 57.12946616, 39.39987171], [79.88472960, 58.59157160, 38.48359563], [79.48271223, 60.05367704, 37.56731954], [79.08069486, 61.51578248, 36.65104345], [78.67867749, 62.97788792, 35.73476736], [78.27666012, 64.43999336, 34.81849127], [77.87464274, 65.90209880, 33.90221519], [77.47262537, 67.36420425, 32.98593910], [77.07060800, 68.82630969, 32.06966301], [76.66859063, 70.28841513, 31.15338692], [76.26657325, 71.75052057, 30.23711083], [75.86455588, 73.21262601, 29.32083475], [75.46253851, 74.67473145, 28.40455866], [75.06052114, 76.13683689, 27.48828257], [74.65850376, 77.59894233, 26.57200648], [74.25648639, 79.06104777, 25.65573039], [73.85446902, 80.52315321, 24.73945431], [73.45245165, 81.98525865, 23.82317822], [73.05043428, 83.44736409, 22.90690213], [72.64841690, 84.90946954, 21.99062604], [72.24639953, 86.37157498, 21.07434995], [71.84438216, 87.83368042, 20.15807387], [71.44236479, 89.29578586, 19.24179778], [71.04034741, 90.75789130, 18.32552169], [70.63833004, 92.21999674, 17.40924560], [70.23631267, 93.68210218, 16.49296951], [69.83429530, 95.14420762, 15.57669343], [69.43227792, 96.60631306, 14.66041734], [69.03026055, 98.06841850, 13.74414125], [68.62824318, 99.53052394, 12.82786516], [68.22622581, 100.9926294, 11.91158907], [67.82420844, 102.4547348, 10.99531298], [67.42219106, 103.9168403, 10.07903690], [67.02017369, 105.3789457, 9.162760809], [66.61815632, 106.8410511, 8.246484721], [66.21613895, 108.3031566, 7.330208633], [65.81412157, 109.7652620, 6.413932545], [65.41210420, 111.2273675, 5.497656457], [65.01008683, 112.6894729, 4.581380368], [64.60806946, 114.1515784, 3.665104280], [64.20605209, 115.6136838, 2.748828192], [63.80403471, 117.0757892, 1.832552104], [63.40201734, 118.5378947, .9162760162], [62.99999996, 120.0000001, -0.8979507982e-7]], COLOUR(RGB, 1.00000000, 0., 0.)), THICKNESS(3), SCALING(CONSTRAINED))

 (2)
> 

NULL``
> 

L33 := solve(zP3 = zP1, l3)
> 

L111 := solve(subs(l3 = L33, yP3 = yP1), l1)
> 

L333 := subs(l1 = L111, L33)
> 

T11 := solve(subs(l3 = L333, l1 = L111, xP3 = xP1), t1)
> 

L3T := subs(t1 = T11, L333)
> 

L1T := subs(t1 = T11, L111)
> 

LP13 := spacecurve([XT13, YT13, ZT13, t3 = 0 .. 1], color = red, scaling = constrained, thickness = 1)

PLOT3D(CURVES([[89.14619532, 109.5415219, 28.16031418], [88.24525256, 108.8365929, 27.58561389], [87.34430980, 108.1316638, 27.01091360], [86.44336704, 107.4267348, 26.43621331], [85.54242428, 106.7218058, 25.86151302], [84.64148151, 106.0168768, 25.28681273], [83.74053875, 105.3119478, 24.71211244], [82.83959598, 104.6070187, 24.13741215], [81.93865322, 103.9020897, 23.56271186], [81.03771046, 103.1971607, 22.98801157], [80.13676769, 102.4922317, 22.41331128], [79.23582493, 101.7873027, 21.83861099], [78.33488217, 101.0823736, 21.26391070], [77.43393941, 100.3774446, 20.68921041], [76.53299664, 99.67251561, 20.11451012], [75.63205388, 98.96758659, 19.53980983], [74.73111112, 98.26265757, 18.96510954], [73.83016835, 97.55772855, 18.39040925], [72.92922559, 96.85279953, 17.81570896], [72.02828283, 96.14787051, 17.24100866], [71.12734006, 95.44294149, 16.66630837], [70.22639730, 94.73801248, 16.09160808], [69.32545454, 94.03308346, 15.51690779], [68.42451177, 93.32815444, 14.94220750], [67.52356901, 92.62322542, 14.36750721], [66.62262625, 91.91829640, 13.79280692], [65.72168348, 91.21336738, 13.21810663], [64.82074072, 90.50843836, 12.64340634], [63.91979796, 89.80350934, 12.06870605], [63.01885519, 89.09858032, 11.49400576], [62.11791243, 88.39365131, 10.91930547], [61.21696967, 87.68872229, 10.34460518], [60.31602690, 86.98379327, 9.769904891], [59.41508414, 86.27886425, 9.195204600], [58.51414138, 85.57393523, 8.620504310], [57.61319861, 84.86900621, 8.045804020], [56.71225585, 84.16407719, 7.471103729], [55.81131309, 83.45914817, 6.896403439], [54.91037032, 82.75421915, 6.321703149], [54.00942756, 82.04929013, 5.747002858], [53.10848480, 81.34436112, 5.172302568], [52.20754204, 80.63943210, 4.597602278], [51.30659927, 79.93450308, 4.022901987], [50.40565651, 79.22957406, 3.448201697], [49.50471375, 78.52464504, 2.873501407], [48.60377098, 77.81971602, 2.298801116], [47.70282822, 77.11478700, 1.724100826], [46.80188546, 76.40985798, 1.149400536], [45.90094269, 75.70492896, .5747002453], [44.99999991, 74.99999993, -0.5632062994e-7]], COLOUR(RGB, 1.00000000, 0., 0.)), THICKNESS(1), SCALING(CONSTRAINED))

 (3)
> 

NULL

``

> 

display(LP12, LP13, LP32, P1, P2, P3, Kriv1, Kriv2, Kriv3)

 
> 

``
> 

``
> 

``

``
 

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