### DodHamSweep.slf ### Sweep along 20 edges on a Dodecahedron ### CHS 2004/10/15 ### The polyline sweep in SLIDE is not properly done ==> FIX IT ! ### there is a small twist occurring on each segment - ### but there is no reason for it, and when the sweep curve is "open", ### and torsion minimization is enabled, then there should be no twist whatsoever! ### I suspect a bad mapping of the profile through the joint! # # The way this _should_ be done is: # look at the "sweep_curve" (polyline) tangent, TI, of the segment going into a joint # and at TO, the tangent of the segment going out of it. # When sweeping the profile through a joint, # first turn the tangent only through half the total angle change, # so that it is then perpendicular to the angle bisector plane at that joint. # Now intersect the prismatic cross section of the incoming beam with this bisector plane # to establish the vertices that need to be generated for forming a properly mitred corner. # # This intersection can be done cheaply, by taking the (constant) cross section # and simply stretching it non-uniformly (in the right direction) # by an amount equal to 1/cos(half angle of turn at joint). # The tricky part is to establich the _direction_ of this non-uniform scaling! # It shoud always be along the normal line which points directly into and out of the joint. # One way to find this direction is to always establish a new coordinate system # at each subsequent joint, so that at the joint the x-axis is always the curve normal # pointing into the turn made by the sweep curve at that joint. # Let's further assume that the z-axis is always in the forward direction of the tangent. # Then the actual turn of the sweep path at the joint is a turn around the local y axis. # # Now, as we go from one joint to the next, this local (Frenet-) frame # of the polyline sweep curve may need to make a torsional twist around the z-axis, # so as to align the x-axis with the normal in each joint. # The amount of the necessary twisting is determined by projecting the normal vector # from the previous joint and also the one from the current joint onto the normal plane # of the sweep segment going into the current joint # and measuring the angle between them in that normal plane. # The cross sectional profile can now be rotated in its defining x-y-plane # by this amount, and then be temporarily stretched by 1/cos(half-angle), # to define where the vertices of this mitred beam corner must be placed in 3D spce. # # I suspect that there might be something wrong with this angle calculation. ############################################################################# tclinit { set winName .slfWINDOW source SLIDEUI.tcl source MATH.tcl proc CreateSliders { parent name } { set subname "slf_[subst \$name]" if { \$parent == {} } { set root .\$subname } elseif { \$parent == "." } { set root .\$subname } else { set root \$parent.\$subname } toplevel \$root set profile [CreateScale \$name \$root profile "profile" 2.0 0.1 4.0 0.1 1 horizontal] set azim [CreateScale \$name \$root azim "azimuth" 0 -270 270 1 1 horizontal] set twist [CreateScale \$name \$root twist "overall twist" 0 -180 180 0.1 1 horizontal] pack \$profile \$azim \$twist -side top -fill x } CreateSliders \$winName slider } #################### # Profile #################### point Y ( 0 {expr \$slider_profile*0.1} 0) endpoint point A ( {expr -\$slider_profile*0.1} 0 0) endpoint point B ( 0 {expr -\$slider_profile*0.2} 0 ) endpoint point X ( {expr \$slider_profile*0.1} 0 0 ) endpoint polyline crossx pointlist ( B X Y A B ) endpolyline crosssection profile type polyline crossx endcrosssection crosssection circ type circle radius {expr \$slider_profile*0.1} slices 4 endcrosssection #################### # Path #################### point Zx ( 0.381966 0 1 ) endpoint point Za ( -0.381966 0 1 ) endpoint point Xy ( 1 0.381966 0 ) endpoint point Xb ( 1 -0.381966 0 ) endpoint point Ay ( -1 0.381966 0 ) endpoint point Ab ( -1 -0.381966 0 ) endpoint point Yz ( 0 1 0.381966 ) endpoint point YY ( 0 1 0.1) endpoint point Y0 ( 0 1 0) endpoint point Yc ( 0 1 -0.381966 ) endpoint point Bz ( 0 -1 0.381966 ) endpoint point Bc ( 0 -1 -0.381966 ) endpoint point Cx ( 0.381966 0 -1 ) endpoint point Ca ( -0.381966 0 -1 ) endpoint point XYZ ( 0.618034 0.618034 0.618034 ) endpoint point XBZ ( 0.618034 -0.618034 0.618034 ) endpoint point AYZ ( -0.618034 0.618034 0.618034 ) endpoint point ABZ ( -0.618034 -0.618034 0.618034 ) endpoint point XYC ( 0.618034 0.618034 -0.618034 ) endpoint point XBC ( 0.618034 -0.618034 -0.618034 ) endpoint point AYC ( -0.618034 0.618034 -0.618034 ) endpoint point ABC ( -0.618034 -0.618034 -0.618034 ) endpoint polyline hampath pointlist ( Y0 YY Yz AYZ Ay AYC Ca Cx XBC Xb XBZ Bz Bc ABC Ab ABZ Za Zx XYZ Xy XYC Yc Y0 ) endpolyline sweep beam path hampath minimizetorsion 1 ## these two together should garantee that no segment is twisted !! closed 0 azimuth {expr \$slider_azim} twist {expr \$slider_twist} ## of course this must be kept at zero ! endpath crosssection profile #crosssection circ endcrosssection #solid SLF_HOLLOW endsweep ########################################################### group assembly instance beam surface Y endinstance (* instance beam surface G rotate( 0.309006 0.5 0 )(36) translate(0.894402 1.447238 0) endinstance *) endgroup #################### VIEWING ############################### surface K color (0.0 0.0 0.0) endsurface surface R color (0.9 0.0 0.0) endsurface surface B color (0.0 0.0 1.0) endsurface surface Y color (1.0 1.0 0.1) endsurface surface W color (1.0 1.0 1.0) endsurface surface C color (0.0 1.0 1.0) endsurface surface G color (0.0 1.0 0.0) endsurface surface M color (1.0 0.0 1.0) endsurface surface O color (1.0 0.6 0.0) endsurface surface X color (0.5 0.5 0.5) endsurface group World instance assembly scale (0.15 0.15 0.15) #shading SLF_WIRE endinstance endgroup #### CAMERA camera cam projection SLF_PARALLEL #projection SLF_PERSPECTIVE frustum (-0.2 -0.2 -2) (0.2 0.2 -0.2) endcamera group gCamera instance cam id instCam translate (0.0 0.0 1.0) endinstance endgroup #### LIGHT light lite type SLF_DIRECTIONAL endlight group gLight0 instance lite id instLite0 lookat eye (1.0 1.0 1.0) target (0.0 0.0 0.0) up (0.0 1.0 0.0) endlookat endinstance endgroup group gLight1 instance lite id instLite1 lookat eye (-1.0 -1.0 0.0) target (0.0 0.0 0.0) up (0.0 1.0 0.0) endlookat endinstance endgroup light lite2 type SLF_AMBIENT color (0.3 0.3 0.3) endlight group gLight2 instance lite2 id instLite2 endinstance endgroup #### RENDER window WINDOW background (0.1 0.2 0.4) endwindow viewport VIEWPORT WINDOW origin (0.0 0.0) size (1.0 1.0) endviewport render VIEWPORT gCamera.instCam.cam World light gLight0.instLite0.lite light gLight1.instLite1.lite light gLight2.instLite2.lite2 endrender ######################################################################