"""Piers under the first helix loop: -15 in deck to the UNDERSIDE of the 3/4 in roadbed (mm). Post 1 (butt joint, bracket 0): P1 top = 1-1/32 in above the deck (template-fit), so the underside is 1-1/32 - 3/4 = 9/32 in. Each later post is 45 deg on = +1/2 in. Post 1 already sits on the cork-transition shim and Post 8 falls over the raised entry tongue, so piers are made for POSTS (2..7) only; edit POSTS to add or drop any. Frame: X radial (+ = outward), Y along the track (+ = uphill), Z up. The top is a plane sloped at the helix grade at the pier's center radius R_C. Height is set at the pier center, which goes on the post's radial line. The arrows engraved on the tabs point uphill. Trellis, built to print fast with no supports: two thin webs run along the track joined by a cross web (an H in plan), each web pierced with 45-degree diamond windows. Each long web carries a 9 mm top flange flared out at 45 degrees; the plywood bears on the two flanges. Webs are WEB_T thick so the slicer fills them with perimeters only (no infill). Every overhang is 45 degrees or steeper. Screws: a tab on each radial side, 3/8 in thick, with a hole countersunk from the top for a #6 drywall screw driven down into the deck. A 1 in screw goes 5/8 in into 3/4 in plywood; a 1-1/4 in screw would come out the bottom. Screw the piers down before the roadbed goes on. Prints feet-down as modeled. """ import numpy as np import trimesh from shapely.geometry import box, Polygon from shapely import affinity from make_height_spacers import IN, revolve, check from stl_text import text_polys, centered OUT = "/Users/lnevo/Downloads/stl/" P1_TOP_IN, PLY_IN, RISE_PER_POST = 1.03125, 0.75, 0.5 POSTS = [2, 3, 4, 5, 6, 7] R_C = (26.0 + 31.75) / 2 # pier center radius, in GRADE = 4.0 / (2 * np.pi * R_C) # helix grade at R_C (rise/run) PIER_W, PIER_L = 2.0 * IN, 1.5 * IN # outside of the flanges: radial width, length along track WEB_T = 2.4 # web thickness (3 perimeters at 0.4-0.45 mm) FLANGE_W, FLANGE_T = 9.0, 1.6 # top flange width, min thickness (at the low end) DIA_A, DIA_GAP, DIA_EDGE = 5.5, 2.0, 2.5 # diamond half-diagonal, tip-to-tip gap, min edge margin FOOT_EXT, FOOT_T = 1.0 * IN, 0.375 * IN # tab reach past the pier, thickness TAB_L = 0.75 * IN # tab length along the track HOLE_OFF = 0.6 * IN # hole center out from the pier's outer face SHAFT_D, HEAD_D, CSK_ANGLE = 0.156 * IN, 0.340 * IN, 90.0 LABEL_SIZE, LABEL_DEPTH = 5.0, 0.6 CORNER_R = 3.0 def underside_in(post): return P1_TOP_IN - PLY_IN + RISE_PER_POST * (post - 1) def prism_y(poly_xz, y0, y1): """Extrude a polygon drawn in (x, z) along Y from y0 to y1.""" m = trimesh.creation.extrude_polygon(poly_xz, y1 - y0) # local (x, z, y) m.apply_transform([[1, 0, 0, 0], [0, 0, 1, y0], [0, 1, 0, 0], [0, 0, 0, 1]]) return m def prism_x(poly_yz, x0, x1): """Extrude a polygon drawn in (y, z) along X from x0 to x1.""" m = trimesh.creation.extrude_polygon(poly_yz, x1 - x0) # local (y, z, x) m.apply_transform([[0, 0, 1, x0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1]]) return m def diamonds(s0, s1, z0, z1): """45-degree diamond windows (2D polys) filling [s0, s1] x [z0, z1] on a square grid.""" a, pitch = DIA_A, 2 * DIA_A + DIA_GAP ncol = max(0, int((s1 - s0 + DIA_GAP) // pitch)) nrow = max(0, int((z1 - z0 + DIA_GAP) // pitch)) out = [] for i in range(ncol): u = s0 + (s1 - s0 - (ncol * pitch - DIA_GAP)) / 2 + a + i * pitch for j in range(nrow): v = z0 + (z1 - z0 - (nrow * pitch - DIA_GAP)) / 2 + a + j * pitch out.append(Polygon([(u, v - a), (u + a, v), (u, v + a), (u - a, v)])) return out def countersink(x, y, top): r_s, r_h = SHAFT_D / 2, HEAD_D / 2 depth = (r_h - r_s) / np.tan(np.radians(CSK_ANGLE / 2)) return revolve([(0, -top - 1), (r_s, -top - 1), (r_s, -depth), (r_h, 0), (r_h, 5), (0, 5)], x, y, top) def tab_label(s, x, rot_deg): """Engraving cutters on a tab's top face; rot_deg turns the text so it runs along Y.""" g = centered(text_polys(s, LABEL_SIZE), 0, 0) g = affinity.translate(affinity.rotate(g, rot_deg, origin=(0, 0)), x, 0) cuts = [] for poly in getattr(g, "geoms", [g]): m = trimesh.creation.extrude_polygon(poly, LABEL_DEPTH + 0.3) m.apply_translation([0, 0, FOOT_T - LABEL_DEPTH]) cuts.append(m) return cuts def pier(post): hc = underside_in(post) * IN low = hc - GRADE * PIER_L / 2 high = hc + GRADE * PIER_L / 2 ztop = high + 1.0 # build tall, then cut to the sloped plane flare = (FLANGE_W - WEB_T) / 2 # 45-degree flare: height = horizontal reach z_flare = low - FLANGE_T - flare # where the flange flare starts assert z_flare > FOOT_T, (post, z_flare) ys = (-PIER_L / 2, PIER_L / 2) parts, cuts = [], [] xw = PIER_W / 2 - FLANGE_W / 2 # web centerline: flange flush with the pier's outside for sx in (1, -1): c = sx * xw prof = Polygon([(c - WEB_T / 2, 0), (c + WEB_T / 2, 0), (c + WEB_T / 2, z_flare), (c + FLANGE_W / 2, z_flare + flare), (c + FLANGE_W / 2, ztop), (c - FLANGE_W / 2, ztop), (c - FLANGE_W / 2, z_flare + flare), (c - WEB_T / 2, z_flare)]) parts.append(prism_y(prof, *ys)) # windows in the long web, one field each side of the cross web, clear of the tab and flare zw0, zw1 = FOOT_T + DIA_EDGE, z_flare - DIA_EDGE for s0, s1 in ((-PIER_L / 2 + DIA_EDGE, -WEB_T / 2 - DIA_EDGE), (WEB_T / 2 + DIA_EDGE, PIER_L / 2 - DIA_EDGE)): for d in diamonds(s0, s1, zw0, zw1): cuts.append(prism_x(d, c - WEB_T, c + WEB_T)) # cross web along X at y = 0, between the long webs, up to the sloped top xi = xw - WEB_T / 2 parts.append(prism_x(box(-WEB_T / 2, 0, WEB_T / 2, ztop), -xi - 0.1, xi + 0.1)) for d in diamonds(-xi + DIA_EDGE, xi - DIA_EDGE, DIA_EDGE + 1.0, low - 2 * DIA_EDGE): cuts.append(prism_y(d, -WEB_T, WEB_T)) # screw tabs from the web out past the hole for sx in (1, -1): x0, x1 = sorted((sx * (xw - WEB_T / 2), sx * (PIER_W / 2 + FOOT_EXT))) parts.append(trimesh.creation.extrude_polygon( box(x0, -TAB_L / 2, x1, TAB_L / 2).buffer(-CORNER_R).buffer(CORNER_R, resolution=16), FOOT_T)) cuts.append(countersink(sx * (PIER_W / 2 + HOLE_OFF), 0, FOOT_T)) # label between the pier and the hole, running uphill (+Y), readable from that side lx = sx * (PIER_W / 2 + (HOLE_OFF - HEAD_D / 2) / 2) cuts += tab_label(f"P{post} →" if sx > 0 else f"← P{post}", lx, 90 if sx > 0 else -90) m = trimesh.boolean.union(parts, engine="manifold") # sloped top: remove everything above z = hc + GRADE*y big = 4 * PIER_W above = trimesh.convex.convex_hull(np.array( [[x, y, hc + GRADE * y + dz] for x in (-big, big) for y in (-big, big) for dz in (0, 200)])) m = trimesh.boolean.difference([m, above] + cuts, engine="manifold") return m, hc if __name__ == "__main__": print(f"grade at r={R_C:.3f} in: {GRADE * 100:.3f}% (top drops/rises {GRADE * PIER_L / IN:.4f} in end to end)") for p in POSTS: m, hc = pier(p) name = f"first_loop_pier_post{p}.stl" check(m, name) print(f" underside at center {hc / IN:.5f} in = {hc:.3f} mm, volume {m.volume / 1000:.1f} cm3") m.export(OUT + name)