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+%
+% Very simple model of my hand
+%
+% Gene Ressler
+%
+% In particular, this completely ignores the carpal joints.
+%
+% Try this with various options to sketch.
+%
+% -D fist \
+% -D ok > none or one of these
+% -D spread /
+%
+% -D topview \
+% -D frontview > none or one of these
+% -D sideview /
+%
+% -D repeated
+%
+% I am not responsible for modifications to draw
+% obscene gestures.
+
+% parameterization of model
+
+% for fingers, 0 is thumb, 1 is index,
+% 2 is middle, 3 is ring, 4 is little
+
+% lateral angle between fingers
+def spread_rot
+ <fist> 0
+ <ok> 5
+ <spread>10
+ <> 0
+% and between thumb and index finger
+def spread_rot_0
+ <fist> 40
+ <ok> 55
+ <spread> 55
+ <> 25
+
+% rotations of finger parts
+% distal is the finger tip
+% middle is below that
+% meta is the knuckle
+def distal_0_rot
+ <fist> 60
+ <ok> 45
+ <> -10
+def middle_0_rot
+ <fist> 50
+ <ok> 40
+ <spread> 0
+ <> 10
+def meta_0_rot
+ <fist> 40
+ <ok> 35
+ <> 0
+
+def distal_1_rot
+ <fist> 90
+ <ok> 54
+ <> 0
+def meta_1_rot
+ <fist> 90
+ <ok> 60
+ <> 0
+
+def distal_2_rot
+ <fist> 90
+ <ok> 30
+ <> 0
+def meta_2_rot
+ <fist> 90
+ <ok> 35
+ <> 0
+
+def distal_3_rot
+ <fist> 90
+ <ok> 30
+ <> 0
+def meta_3_rot
+ <fist> 90
+ <ok> 30
+ <> 0
+
+def distal_4_rot
+ <fist> 90
+ <ok> 30
+ <> 0
+def meta_4_rot
+ <fist> 90
+ <ok> 25
+ <> 0
+
+% end parameters
+
+% useful stuff
+def O (0,0,0)
+def I [1,0,0]
+def J [0,1,0]
+def K [0,0,1]
+
+% dependent rotations
+% fingers have the last two joints wired together
+def middle_1_rot distal_1_rot
+def middle_2_rot distal_2_rot
+def middle_3_rot distal_3_rot
+def middle_4_rot distal_4_rot
+
+% proportions
+def proximal_rad .6
+def distal_rad .5
+def distal_len 1.8
+def joint_rad .6
+def joint_gap .7
+def middle_ratio 1.8
+def proximal_distal_ratio proximal_rad / distal_rad
+
+% primitive segment of a finger is a truncated cone
+def segment {
+ def n_faces 8
+ sweep { n_faces<>, rotate(360 / n_faces, [J]) }
+ line(proximal_rad, 0)(distal_rad, distal_len)
+}
+
+% spheres to connect segments at joints
+def joint_sphere {
+ def n_joint_faces 8
+ sweep [fillcolor=lightgray] { n_joint_faces, rotate(360 / n_joint_faces, [J]) }
+ sweep { n_joint_faces, rotate(180 / n_joint_faces) }
+ (0, -joint_rad)
+}
+
+% following is five separate definitions for five fingers
+% with parameters, this would be much shorter!
+
+def distal_0 {
+ put { translate(joint_gap * joint_rad * [J])
+ then rotate(distal_0_rot, [I])
+ then translate((distal_len + joint_gap * joint_rad) * [J]) }
+ {segment}
+ put { rotate(distal_0_rot / 2, [I])
+ then translate((distal_len + joint_gap * joint_rad) * [J]) }
+ {joint_sphere}
+ put { scale( [J] + proximal_distal_ratio * ([I]+[K]) ) }
+ {segment}
+}
+
+def finger_0 {
+ put { translate(joint_gap * joint_rad * [J])
+ then rotate(middle_0_rot, [I])
+ then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }
+ {distal_0}
+ put { scale(proximal_distal_ratio)
+ then rotate(middle_0_rot / 2, [I])
+ then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }
+ {joint_sphere}
+ put { scale( middle_ratio * [J] + proximal_distal_ratio^2 * ([I]+[K]) ) }
+ {segment}
+}
+
+def distal_1 {
+ put { translate(joint_gap * joint_rad * [J])
+ then rotate(distal_1_rot, [I])
+ then translate((distal_len + joint_gap * joint_rad) * [J]) }
+ {segment}
+ put { rotate(distal_1_rot / 2, [I])
+ then translate((distal_len + joint_gap * joint_rad) * [J]) }
+ {joint_sphere}
+ put { scale( [J] + proximal_distal_ratio * ([I]+[K]) ) }
+ {segment}
+}
+
+def finger_1 {
+ put { translate(joint_gap * joint_rad * [J])
+ then rotate(middle_1_rot, [I])
+ then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }
+ {distal_1}
+ put { scale(proximal_distal_ratio)
+ then rotate(middle_1_rot / 2, [I])
+ then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }
+ {joint_sphere}
+ put { scale( middle_ratio * [J] + proximal_distal_ratio^2 * ([I]+[K]) ) }
+ {segment}
+}
+
+def distal_2 {
+ put { translate(joint_gap * joint_rad * [J])
+ then rotate(distal_2_rot, [I])
+ then translate((distal_len + joint_gap * joint_rad) * [J]) }
+ {segment}
+ put { rotate(distal_2_rot / 2, [I])
+ then translate((distal_len + joint_gap * joint_rad) * [J]) }
+ {joint_sphere}
+ put { scale( [J] + proximal_distal_ratio * ([I]+[K]) ) }
+ {segment}
+}
+
+def finger_2 {
+ put { translate(joint_gap * joint_rad * [J])
+ then rotate(middle_2_rot, [I])
+ then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }
+ {distal_2}
+ put { scale(proximal_distal_ratio)
+ then rotate(middle_2_rot / 2, [I])
+ then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }
+ {joint_sphere}
+ put { scale( middle_ratio * [J] + proximal_distal_ratio^2 * ([I]+[K]) ) }
+ {segment}
+}
+
+def distal_3 {
+ put { translate(joint_gap * joint_rad * [J])
+ then rotate(distal_3_rot, [I])
+ then translate((distal_len + joint_gap * joint_rad) * [J]) }
+ {segment}
+ put { rotate(distal_3_rot / 2, [I])
+ then translate((distal_len + joint_gap * joint_rad) * [J]) }
+ {joint_sphere}
+ put { scale( [J] + proximal_distal_ratio * ([I]+[K]) ) }
+ {segment}
+}
+
+def finger_3 {
+ put { translate(joint_gap * joint_rad * [J])
+ then rotate(middle_3_rot, [I])
+ then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }
+ {distal_3}
+ put { scale(proximal_distal_ratio)
+ then rotate(middle_3_rot / 2, [I])
+ then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }
+ {joint_sphere}
+ put { scale( middle_ratio * [J] + proximal_distal_ratio^2 * ([I]+[K]) ) }
+ {segment}
+}
+
+def distal_4 {
+ put { translate(joint_gap * joint_rad * [J])
+ then rotate(distal_4_rot, [I])
+ then translate((distal_len + joint_gap * joint_rad) * [J]) }
+ {segment}
+ put { rotate(distal_4_rot / 2, [I])
+ then translate((distal_len + joint_gap * joint_rad) * [J]) }
+ {joint_sphere}
+ put { scale( [J] + proximal_distal_ratio * ([I]+[K]) ) }
+ {segment}
+}
+
+def finger_4 {
+ put { translate(joint_gap * joint_rad * [J])
+ then rotate(middle_4_rot, [I])
+ then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }
+ {distal_4}
+ put { scale(proximal_distal_ratio)
+ then rotate(middle_4_rot / 2, [I])
+ then translate((middle_ratio * distal_len + joint_gap * joint_rad) * [J]) }
+ {joint_sphere}
+ put { scale( middle_ratio * [J] + proximal_distal_ratio^2 * ([I]+[K]) ) }
+ {segment}
+}
+
+% points on the palm of the hand
+def proximal_0_loc (1.8,-5.5,0)
+def proximal_1_loc (1.8,.1,0)
+def proximal_2_loc (O)
+def proximal_3_loc (-1.8,-.2,0)
+def proximal_4_loc (-3.6,-.5,0)
+def h5 (proximal_4_loc) + [-.6,-.2]
+def h6 (h5) + [1,-5]
+def h8 (proximal_0_loc) + [.75,-.5]
+def h7 (h8) + [-.6,-.8]
+def h6a (h6) + .6 * ((h7) - (h6))
+def h9 (h8) + [-1.9,1]
+def h10 (proximal_1_loc) + [.85,-.3]
+
+def hand {
+
+ % thumb has an extra rotation for opposable-ness!
+ def opposition_rot rotate(-50, [J])
+ def thk_scale_0 1.2
+ put { scale([thk_scale_0,.9,thk_scale_0]) % this distorts a little; oh well
+ then translate((joint_gap * joint_rad) * [J])
+ then [[opposition_rot]]
+ then rotate(meta_0_rot, [I])
+ then rotate(-spread_rot_0, [K])
+ then translate((proximal_0_loc) - (O)) }
+ {finger_0}
+
+ put { scale(thk_scale_0 * proximal_distal_ratio^2)
+ then [[opposition_rot]]
+ then rotate(meta_0_rot / 2, [I])
+ then rotate(-spread_rot_0, [K])
+ then translate((proximal_0_loc) - (O)) }
+ {joint_sphere}
+
+ % index finger
+ def scale_1 .85
+ put { scale(scale_1)
+ then translate((joint_gap * joint_rad) * [J])
+ then rotate(meta_1_rot, [I])
+ then rotate(-spread_rot, [K])
+ then translate((proximal_1_loc) - (O)) }
+ {finger_1}
+
+ put { scale(scale_1 * proximal_distal_ratio^2)
+ then rotate(meta_1_rot / 2, [I])
+ then rotate(-spread_rot, [K])
+ then translate((proximal_1_loc) - (O)) }
+ {joint_sphere}
+
+ % middle finger
+ put { % no scale then
+ translate((joint_gap * joint_rad) * [J])
+ then rotate(meta_2_rot, [I])
+ % no spread rotation
+ then translate((proximal_2_loc) - (O)) }
+ {finger_2}
+
+ put { scale(proximal_distal_ratio^2)
+ then rotate(meta_2_rot / 2, [I])
+ then rotate(-spread_rot, [K])
+ then translate((proximal_2_loc) - (O)) }
+ {joint_sphere}
+
+ % ring finger
+ def scale_3 .85
+ put { scale(scale_3)
+ then translate((joint_gap * joint_rad) * [J])
+ then rotate(meta_3_rot, [I])
+ then rotate(spread_rot, [K])
+ then translate((proximal_3_loc) - (O)) }
+ {finger_3}
+
+ put { scale(scale_3 * proximal_distal_ratio^2)
+ then rotate(meta_3_rot / 2, [I])
+ then rotate(-spread_rot, [K])
+ then translate((proximal_3_loc) - (O)) }
+ {joint_sphere}
+
+ % little finger
+ def scale_4 .7
+ put { scale(scale_4)
+ then translate((joint_gap * joint_rad) * [J])
+ then rotate(meta_4_rot, [I])
+ then rotate(2 * spread_rot, [K])
+ then translate((proximal_4_loc) - (O)) }
+ {finger_4}
+
+ put { scale(scale_4 * proximal_distal_ratio^2)
+ then rotate(meta_4_rot / 2, [I])
+ then rotate(-spread_rot, [K])
+ then translate((proximal_4_loc) - (O)) }
+ {joint_sphere}
+
+ % palm is built by sweeping a polygon through a small
+ % angle in order to make it thicker at the wrist
+ put { translate(joint_gap * joint_rad * -[J]) } % drop polytope to expose knuckles
+ sweep { 1, rotate(6, (0,15,0), [I]) }
+ put { rotate(-3, (0,15,0), [I]) } {
+ % need two polygons for convexity; the desired shape is concave at the thumb
+ polygon(proximal_1_loc)(proximal_2_loc)(proximal_3_loc)(proximal_4_loc)
+ (h5)(h6)(h6a)(h9)(h10)
+ polygon(h6a)(h7)(h8)(h9)
+ }
+}
+
+% a few views
+def viewxf
+ <frontview> view((0,0,10))
+ <sideview> view((10,0,0))
+ <topview> view((0,10,0), (O), -[K])
+ <> view((4,3,10))
+
+% either a single copy or a repeat to show different angles
+def scene
+ <repeated>
+ put { [[viewxf]] then scale(.25) } {
+ def N 4
+ repeat { N, rotate(270/N, [3,2,1]), translate(14*[I]) } {hand}
+ }
+ <> put { [[viewxf]] then scale(.3) } {hand}
+
+{scene}
+
+global {
+ set [linewidth=.3pt]
+}