From 743cb29fdecb86f4ebce4984761866b95fa29fcb Mon Sep 17 00:00:00 2001 From: "DESKTOP-B184KCC\\Zyl" Date: Fri, 31 May 2024 21:40:01 +0200 Subject: [PATCH] Ensure equal edge lengths within edge loops --- CHANGES.md | 5 ++ README.md | 4 +- __init__.py | 2 +- add_mesh_even_quad_sphere.py | 168 ++++++++++++++++++----------------- img/even_quad_sphere.png | Bin 430064 -> 324611 bytes 5 files changed, 95 insertions(+), 84 deletions(-) create mode 100644 CHANGES.md diff --git a/CHANGES.md b/CHANGES.md new file mode 100644 index 0000000..d725b47 --- /dev/null +++ b/CHANGES.md @@ -0,0 +1,5 @@ +# 1.1 (2024-06-05) +* Rewrote math to guarantee equal edge length within all edge loops instead of just the edges of the three axis-aligned circles within the sphere. + +# 1.0 (2024-04-29) +* Initial release. diff --git a/README.md b/README.md index 98293e3..7b44f15 100644 --- a/README.md +++ b/README.md @@ -1,12 +1,12 @@ # Even Quad Sphere -Special case of quad sphere which maximizes equality of edge lengths. +Special case of quad sphere which makes lengths of edges within same edge loops equal. Quad sphere from "Extra Objects" addon (unequal edge lengths even on axis-aligned circles): ![Addon preferences](img/quad_sphere_extra_objects_addon.png "Extra Objects addon quad sphere") -Quad sphere from this addon (equal edge lengths on axis-aligned circles): +Quad sphere from this addon (equal edge lengths of edges within same edge loops): ![Addon preferences](img/even_quad_sphere.png "Quad sphere made by this addon") diff --git a/__init__.py b/__init__.py index 90fbd80..16304cc 100644 --- a/__init__.py +++ b/__init__.py @@ -2,7 +2,7 @@ "name": "Even Quad Sphere", "description": "Special case of quad sphere which maximizes equality of edge lengths", "author": "Zyl", - "version": (1, 0), + "version": (1, 1), "blender": (2, 93, 0), "category": "Add Mesh" } diff --git a/add_mesh_even_quad_sphere.py b/add_mesh_even_quad_sphere.py index de56490..4be9020 100644 --- a/add_mesh_even_quad_sphere.py +++ b/add_mesh_even_quad_sphere.py @@ -1,19 +1,18 @@ import bpy from bpy_extras import object_utils -from itertools import permutations from math import ( - copysign, pi, - sqrt, tan, + pi, sqrt, ) from bpy.types import Operator from bpy.props import ( BoolProperty, - EnumProperty, FloatProperty, - FloatVectorProperty, IntProperty, - StringProperty, ) +from mathutils import ( + Vector, + Quaternion, +) def even_quad_sphere(slices, size): @@ -26,77 +25,77 @@ def even_quad_sphere(slices, size): vertIndex = 0 # Top - for z in range(0, slices + 1): - for x in range(0, slices + 1): - i = x + z * lines + for v in range(0, lines): + for u in range(0, lines): + i = u + v * lines sideVerts[0][i] = vertIndex vertIndex = vertIndex + 1 verts.append([0.0, 0.0, 0.0]) # Front - for y in range(0, slices + 1): - for x in range(0, slices + 1): - i = x + y * lines - if y == slices: - sideVerts[1][i] = sideVerts[0][x] + for v in range(0, lines): + for u in range(0, lines): + i = u + v * lines + if v == lines - 1: + sideVerts[1][i] = sideVerts[0][u] else: sideVerts[1][i] = vertIndex vertIndex = vertIndex + 1 verts.append([0.0, 0.0, 0.0]) # Right - for y in range(0, slices + 1): - for z in range(0, slices + 1): - i = z + y * lines - if z == 0: - sideVerts[2][i] = sideVerts[1][i + slices] - elif y == slices: - sideVerts[2][i] = sideVerts[0][slices + z * lines] + for v in range(0, lines): + for u in range(0, lines): + i = u + v * lines + if u == 0: + sideVerts[2][i] = sideVerts[1][v * lines + lines - 1] + elif v == lines - 1: + sideVerts[2][i] = sideVerts[0][u * lines + lines - 1] else: sideVerts[2][i] = vertIndex vertIndex = vertIndex + 1 verts.append([0.0, 0.0, 0.0]) # Back - for y in range(0, slices + 1): - for x in range(0, slices + 1): - i = x + y * lines - if x == slices: - sideVerts [3][i] = sideVerts[2][i] - elif y == slices: - sideVerts [3][i] = sideVerts[0][i] + for v in range(0, lines): + for u in range(0, lines): + i = u + v * lines + if u == 0: + sideVerts [3][i] = sideVerts[2][i + lines - 1] + elif v == lines - 1: + sideVerts [3][i] = sideVerts[0][lines * lines - 1 - u] else: sideVerts [3][i] = vertIndex vertIndex = vertIndex + 1 verts.append([0.0, 0.0, 0.0]) # Left - for y in range(0, slices + 1): - for z in range(0, slices + 1): - i = z + y * lines - if z == 0: - sideVerts [4][i] = sideVerts [1][i] - elif y == slices: - sideVerts [4][i] = sideVerts [0][z * lines] - elif z == slices: - sideVerts [4][i] = sideVerts [3][i - slices] + for v in range(0, lines): + for u in range(0, lines): + i = u + v * lines + if u == 0: + sideVerts [4][i] = sideVerts [3][i + lines - 1] + elif v == lines - 1: + sideVerts [4][i] = sideVerts [0][(lines - 1 - u) * lines] + elif u == lines - 1: + sideVerts [4][i] = sideVerts [1][i - lines + 1] else: sideVerts [4][i] = vertIndex vertIndex = vertIndex + 1 verts.append([0.0, 0.0, 0.0]) # Bottom - for z in range(0, slices + 1): - for x in range(0, slices + 1): - i = x + z * lines - if z == 0: - sideVerts [5][i] = sideVerts [1][x] - elif z == slices: - sideVerts [5][i] = sideVerts [3][x] - elif x == slices: - sideVerts [5][i] = sideVerts [2][z] - elif x == 0: - sideVerts [5][i] = sideVerts [4][z] + for v in range(0, lines): + for u in range(0, lines): + i = u + v * lines + if v == 0: + sideVerts [5][i] = sideVerts [3][lines - 1 - u] + elif v == lines - 1: + sideVerts [5][i] = sideVerts [1][u] + elif u == 0: + sideVerts [5][i] = sideVerts [4][v] + elif u == lines - 1: + sideVerts [5][i] = sideVerts [2][lines - 1 - v] else: sideVerts [5][i] = vertIndex vertIndex = vertIndex + 1 @@ -105,46 +104,53 @@ def even_quad_sphere(slices, size): faces = [] tempVerts = [] for s in range(0, 6): - invertedWinding = (s == 3) or (s == 4) or (s == 5) for y in range(0, slices): for x in range(0, slices): i = x + y * lines tempVerts.clear() - if invertedWinding: - tempVerts.append(sideVerts[s][i]) - tempVerts.append(sideVerts[s][i + 1]) - tempVerts.append(sideVerts[s][i + 1 + lines]) - tempVerts.append(sideVerts[s][i + lines]) - else: - tempVerts.append(sideVerts[s][i]) - tempVerts.append(sideVerts[s][i + lines]) - tempVerts.append(sideVerts[s][i + lines + 1]) - tempVerts.append(sideVerts[s][i + 1]) + tempVerts.append(sideVerts[s][i]) + tempVerts.append(sideVerts[s][i + 1]) + tempVerts.append(sideVerts[s][i + 1 + lines]) + tempVerts.append(sideVerts[s][i + lines]) faces.append(tuple(tempVerts)) - sides = ((0, 1, 0), (0, 0, -1), (1, 0, 0), (0, 0, 1), (-1, 0, 0), (0, -1, 0)) - xDirections = ((1, 0, 0), (1, 0, 0), (0, 0, 1), (1, 0, 0), (0, 0, 1), (1, 0, 0)) - yDirections = ((0, 0, 1), (0, 1, 0), (0, 1, 0), (0, 1, 0), (0, 1, 0), (0, 0, 1)) - quarterPi = pi / 4 - for s in range(0, 6): - side = sides[s] - xDir = xDirections[s] - yDir = yDirections[s] - for y in range(0, slices + 1): - for x in range(0, slices + 1): - i = x + y * lines + # Top, Front, Right, Back, Left, Bottom + sides = ((0, 0, 1), (0, -1, 0), (1, 0, 0), (0, 1, 0), (-1, 0, 0), (0, 0, -1)) + uDirections = ((1, 0, 0), (1, 0, 0), (0, 1, 0), (-1, 0, 0), (0, -1, 0), (1, 0, 0)) + # vDirections = ((0, 1, 0), (0, 0, 1), (0, 0, 1), (0, 0, 1), (0, 0, 1), (0, -1, 0)) # not used - # Range -1 to 1. - xLinear = (2 * x - slices) / slices - yLinear = (2 * y - slices) / slices - - # More even distribution - xLinear = tan(xLinear * quarterPi) - yLinear = tan(yLinear * quarterPi) - - newPos = [side[i] + xLinear * xDir[i] + yLinear * yDir[i] for i in range(0, 3)] - newPosLen = (newPos[0]*newPos[0] + newPos[1]*newPos[1] + newPos[2]*newPos[2]) ** (1/2) - newPos = [newPos[i] / newPosLen for i in range(0, 3)] + cornerArcAngle = Vector((0, 1, 1)).angle(Vector((1, 1, 1))) + for s in range(0, 6): + side = Vector(sides[s]) + uDir = Vector(uDirections[s]) + # vDir = Vector(vDirections[s]) + for v in range(0, lines): + vLinear = (2 * v - slices) / slices + + p0 = (side - uDir).normalized() + p1 = (side + uDir).normalized() + pCenter = Vector(side) + + p0.rotate(Quaternion(side + uDir, -cornerArcAngle * vLinear)) + p1.rotate(Quaternion(side - uDir, cornerArcAngle * vLinear)) + pCenter.rotate(Quaternion(uDir, -pi / 4 * vLinear)) + + zDelta 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