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+// Geometry functions
+// Copyright (C) 2002 David Rosen
+// Copyright (C) 2023 Nguyễn Gia Phong
+//
+// This file is part of Black Shades.
+//
+// Black Shades is free software: you can redistribute it and/or modify
+// it under the terms of the GNU General Public License as published
+// by the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// Black Shades is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with Black Shades. If not, see <https://www.gnu.org/licenses/>.
+
+const Child = std.meta.Child;
+const std = @import("std");
+
+const c = @import("cimport.zig");
+
+fn sqr(x: anytype) @TypeOf(x) {
+ return x * x;
+}
+
+fn dot(u: anytype, v: @TypeOf(u)) Child(@TypeOf(u)) {
+ return @reduce(.Add, u * v);
+}
+
+export fn sqrlen(v: XYZ) f32 {
+ const u = @bitCast(@Vector(3, f32), v);
+ return dot(u, u);
+}
+
+fn norm(v: anytype) Child(@TypeOf(v)) {
+ return @sqrt(dot(v, v));
+}
+
+const XYZ = extern struct { x: f32, y: f32, z: f32 };
+
+export fn crossProduct(u: XYZ, v: XYZ) XYZ {
+ return .{
+ .x = u.y * v.z - u.z * v.y,
+ .y = u.z * v.x - u.x * v.z,
+ .z = u.x * v.y - u.y * v.x,
+ };
+}
+
+export fn normalize(v: XYZ) XYZ {
+ const u = @bitCast(@Vector(3, f32), v);
+ const d = norm(u);
+ return if (d == 0) v else @bitCast(XYZ, u / @splat(3, d));
+}
+
+export fn reflect(v: XYZ, n: XYZ) XYZ {
+ const u = @bitCast(@Vector(3, f32), v);
+ const m = @bitCast(@Vector(3, f32), n);
+ return @bitCast(XYZ, u - m * @splat(3, dot(u, m) * 2));
+}
+
+export fn segmentIntersectsSphere(a: XYZ, b: XYZ, j: XYZ, r: f32) bool {
+ // FIXME: call directly with vectors
+ const p = @bitCast(@Vector(3, f32), a);
+ const q = @bitCast(@Vector(3, f32), b);
+ const i = @bitCast(@Vector(3, f32), j);
+
+ if (@reduce(.Or, @max(p, q) < i - @splat(3, r))) return false;
+ if (@reduce(.Or, @min(p, q) > i + @splat(3, r))) return false;
+ // https://en.wikipedia.org/wiki/Line–sphere_intersection
+ const d = q - p; // line's direction
+ const u = d / @splat(3, norm(d)); // unit vector
+ return sqr(dot(u, (p - i))) >= @reduce(.Add, sqr(p - i)) - sqr(r);
+}
+
+export fn getFrustum(frustum: [*][4]f32) void {
+ var proj: [16]f32 = undefined;
+ c.glGetFloatv(c.GL_PROJECTION_MATRIX, &proj);
+
+ var mv: [16]f32 = undefined;
+ c.glGetFloatv(c.GL_MODELVIEW_MATRIX, &mv);
+
+ const clip = [16]f32{
+ mv[0] * proj[0] + mv[1] * proj[4] + mv[2] * proj[8] + mv[3] * proj[12],
+ mv[0] * proj[1] + mv[1] * proj[5] + mv[2] * proj[9] + mv[3] * proj[13],
+ mv[0] * proj[2] + mv[1] * proj[6] + mv[2] * proj[10] + mv[3] * proj[14],
+ mv[0] * proj[3] + mv[1] * proj[7] + mv[2] * proj[11] + mv[3] * proj[15],
+ mv[4] * proj[0] + mv[5] * proj[4] + mv[6] * proj[8] + mv[7] * proj[12],
+ mv[4] * proj[1] + mv[5] * proj[5] + mv[6] * proj[9] + mv[7] * proj[13],
+ mv[4] * proj[2] + mv[5] * proj[6] + mv[6] * proj[10] + mv[7] * proj[14],
+ mv[4] * proj[3] + mv[5] * proj[7] + mv[6] * proj[11] + mv[7] * proj[15],
+ mv[8] * proj[0] + mv[9] * proj[4] + mv[10] * proj[8] + mv[11] * proj[12],
+ mv[8] * proj[1] + mv[9] * proj[5] + mv[10] * proj[9] + mv[11] * proj[13],
+ mv[8] * proj[2] + mv[9] * proj[6] + mv[10] * proj[10] + mv[11] * proj[14],
+ mv[8] * proj[3] + mv[9] * proj[7] + mv[10] * proj[11] + mv[11] * proj[15],
+ mv[12] * proj[0] + mv[13] * proj[4] + mv[14] * proj[8] + mv[15] * proj[12],
+ mv[12] * proj[1] + mv[13] * proj[5] + mv[14] * proj[9] + mv[15] * proj[13],
+ mv[12] * proj[2] + mv[13] * proj[6] + mv[14] * proj[10] + mv[15] * proj[14],
+ mv[12] * proj[3] + mv[13] * proj[7] + mv[14] * proj[11] + mv[15] * proj[15],
+ };
+
+ // Right plane
+ frustum[0][0] = clip[3] - clip[0];
+ frustum[0][1] = clip[7] - clip[4];
+ frustum[0][2] = clip[11] - clip[8];
+ frustum[0][3] = clip[15] - clip[12];
+
+ // Left plane
+ frustum[1][0] = clip[3] + clip[0];
+ frustum[1][1] = clip[7] + clip[4];
+ frustum[1][2] = clip[11] + clip[8];
+ frustum[1][3] = clip[15] + clip[12];
+
+ // Bottom plane
+ frustum[2][0] = clip[3] + clip[1];
+ frustum[2][1] = clip[7] + clip[5];
+ frustum[2][2] = clip[11] + clip[9];
+ frustum[2][3] = clip[15] + clip[13];
+
+ // Top plane
+ frustum[3][0] = clip[3] - clip[1];
+ frustum[3][1] = clip[7] - clip[5];
+ frustum[3][2] = clip[11] - clip[9];
+ frustum[3][3] = clip[15] - clip[13];
+
+ // Far plane
+ frustum[4][0] = clip[3] - clip[2];
+ frustum[4][1] = clip[7] - clip[6];
+ frustum[4][2] = clip[11] - clip[10];
+ frustum[4][3] = clip[15] - clip[14];
+
+ // Near plane
+ frustum[5][0] = clip[3] + clip[2];
+ frustum[5][1] = clip[7] + clip[6];
+ frustum[5][2] = clip[11] + clip[10];
+ frustum[5][3] = clip[15] + clip[14];
+
+ // normalize the right plane
+ var t: f32 = undefined;
+ t = @sqrt(frustum[0][0]*frustum[0][0]
+ + frustum[0][1]*frustum[0][1]
+ + frustum[0][2]*frustum[0][2]);
+ frustum[0][0] /= t;
+ frustum[0][1] /= t;
+ frustum[0][2] /= t;
+ frustum[0][3] /= t;
+
+ // calculate left plane
+ frustum[1][0] = clip[3] + clip[0];
+ frustum[1][1] = clip[7] + clip[4];
+ frustum[1][2] = clip[11] + clip[ 8];
+ frustum[1][3] = clip[15] + clip[12];
+
+ // normalize the left plane
+ t = @sqrt(frustum[1][0]*frustum[1][0]
+ + frustum[1][1]*frustum[1][1]
+ + frustum[1][2]*frustum[1][2]);
+ frustum[1][0] /= t;
+ frustum[1][1] /= t;
+ frustum[1][2] /= t;
+ frustum[1][3] /= t;
+
+ // calculate the bottom plane
+ frustum[2][0] = clip[3] + clip[1];
+ frustum[2][1] = clip[7] + clip[5];
+ frustum[2][2] = clip[11] + clip[9];
+ frustum[2][3] = clip[15] + clip[13];
+
+ // normalize the bottom plane
+ t = @sqrt(frustum[2][0]*frustum[2][0]
+ + frustum[2][1]*frustum[2][1]
+ + frustum[2][2]*frustum[2][2]);
+ frustum[2][0] /= t;
+ frustum[2][1] /= t;
+ frustum[2][2] /= t;
+ frustum[2][3] /= t;
+
+ // calculate the top plane
+ frustum[3][0] = clip[3] - clip[1];
+ frustum[3][1] = clip[7] - clip[5];
+ frustum[3][2] = clip[11] - clip[9];
+ frustum[3][3] = clip[15] - clip[13];
+
+ // normalize the top plane
+ t = @sqrt(frustum[3][0]*frustum[3][0]
+ + frustum[3][1]*frustum[3][1]
+ + frustum[3][2]*frustum[3][2]);
+ frustum[3][0] /= t;
+ frustum[3][1] /= t;
+ frustum[3][2] /= t;
+ frustum[3][3] /= t;
+
+ // calculate the far plane
+ frustum[4][0] = clip[3] - clip[2];
+ frustum[4][1] = clip[7] - clip[6];
+ frustum[4][2] = clip[11] - clip[10];
+ frustum[4][3] = clip[15] - clip[14];
+
+ // normalize the far plane
+ t = @sqrt(frustum[4][0]*frustum[4][0]
+ + frustum[4][1]*frustum[4][1]
+ + frustum[4][2]*frustum[4][2]);
+ frustum[4][0] /= t;
+ frustum[4][1] /= t;
+ frustum[4][2] /= t;
+ frustum[4][3] /= t;
+
+ // calculate the near plane
+ frustum[5][0] = clip[3] + clip[2];
+ frustum[5][1] = clip[7] + clip[6];
+ frustum[5][2] = clip[11] + clip[10];
+ frustum[5][3] = clip[15] + clip[14];
+
+ // normalize the near plane
+ t = @sqrt(frustum[5][0]*frustum[5][0]
+ + frustum[5][1]*frustum[5][1]
+ + frustum[5][2]*frustum[5][2]);
+ frustum[5][0] /= t;
+ frustum[5][1] /= t;
+ frustum[5][2] /= t;
+ frustum[5][3] /= t;
+}
+
+export fn cubeInFrustum(frustum: [*][4]f32,
+ x: f32, y: f32, z: f32, size: f32) bool {
+ const delta = [_]f32{ -size, size };
+ var i = @as(u8, 0);
+ loop: while (i < 6) : (i += 1) {
+ for (delta) |dx| for (delta) |dy| for (delta) |dz|
+ if (frustum[i][0] * (x + dx) + frustum[i][1] * (y + dy)
+ + frustum[i][2] * (z + dz) + frustum[i][3] > 0) continue :loop;
+ return false;
+ }
+ return true;
+}
+
+export fn sphereInFrustum(frustum: [*][4]f32,
+ x: f32, y: f32, z: f32, r: f32) bool {
+ var i = @as(u8, 0);
+ while (i < 6) : (i += 1)
+ if (frustum[i][0] * x + frustum[i][1] * y
+ + frustum[i][2] * z + frustum[i][3] <= -r)
+ return false;
+ return true;
+}
generated by cgit v1.2.3 (git 2.25.1) at 2026-01-23 11:02:32 +0000