From cf7eff7aab751fd1b599d967ee156c7ebb61cbbd Mon Sep 17 00:00:00 2001
From: Franklin Wei <me@fwei.tk>
Date: Mon, 4 Feb 2019 18:16:49 -0500
Subject: Work on adding toroid

---
 curve.cpp | 89 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 80 insertions(+), 9 deletions(-)

(limited to 'curve.cpp')

diff --git a/curve.cpp b/curve.cpp
index 73f40c1..c71a8c3 100644
--- a/curve.cpp
+++ b/curve.cpp
@@ -4,15 +4,15 @@
 
 using namespace std;
 
-vec3 LineSegment::integrate(vec3 (*integrand)(vec3 s, vec3 ds), double dl)
+vec3 LineSegment::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
 {
     vec3 diff = this->b - this->a, sum = 0;
 
-    double len = diff.magnitude();
+    scalar len = diff.magnitude();
 
     vec3 diffnorm = diff / len, s = this->a, ds = diffnorm * dl;
 
-    double l;
+    scalar l;
 
     for(l = 0; l < len; l += dl, s += ds)
         sum += integrand(s, ds);
@@ -23,11 +23,11 @@ vec3 LineSegment::integrate(vec3 (*integrand)(vec3 s, vec3 ds), double dl)
     return sum;
 }
 
-vec3 Arc::integrate(vec3 (*integrand)(vec3 s, vec3 ds), double dl)
+vec3 Arc::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
 {
     //cout << "Integrating loop of length " << this->angle << " radians" << endl;
 
-    double r = this->radius.magnitude(), dtheta = dl / r;
+    scalar r = this->radius.magnitude(), dtheta = dl / r;
 
     //cout << "R = " << r << ", dtheta = " << dtheta << endl;
 
@@ -35,7 +35,7 @@ vec3 Arc::integrate(vec3 (*integrand)(vec3 s, vec3 ds), double dl)
 
     //cout << "rot = " << rot << ", crot = " << crot << endl;
 
-    double len = this->angle * r, l;
+    scalar len = this->angle * r, l;
 
     vec3 sum = 0;
 
@@ -63,11 +63,11 @@ vec3 Arc::integrate(vec3 (*integrand)(vec3 s, vec3 ds), double dl)
     return sum;
 }
 
-vec3 Spiral::integrate(vec3 (*integrand)(vec3 s, vec3 ds), double dl)
+vec3 Spiral::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
 {
     //cout << "Integrating loop of length " << this->angle << " radians" << endl;
 
-    double r = this->radius.magnitude(), dtheta = dl / r;
+    scalar r = this->radius.magnitude(), dtheta = dl / r;
 
     //cout << "R = " << r << ", dtheta = " << dtheta << endl;
 
@@ -75,7 +75,8 @@ vec3 Spiral::integrate(vec3 (*integrand)(vec3 s, vec3 ds), double dl)
 
     //cout << "rot = " << rot << ", crot = " << crot << endl;
 
-    double len = this->angle * r, l;
+    /* only flat (doesn't include stretched length) */
+    scalar len = this->angle * r, l;
 
     vec3 sum = 0;
 
@@ -110,3 +111,73 @@ vec3 Spiral::integrate(vec3 (*integrand)(vec3 s, vec3 ds), double dl)
 
     return sum;
 }
+
+vec3 Toroid::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
+{
+    /* this applies to the minor rotation */
+    scalar minor_r = this->minor_r;
+
+    scalar major_r = this->major_radius.magnitude();
+
+    /* how far parallel to the major median each dl takes us */
+    scalar dpar = this->pitch * dl / (2 * M_PI * minor_r) * major_r;
+    
+    /* how far each dl rotates the major vector */
+    scalar major_dtheta = dpar / major_r;
+
+    /* how long perpendicular to the major median each dl takes us (from
+     * Pythagoras) */
+    scalar dper = sqrt(dl * dl - dpar * dpar);
+
+    scalar minor_dtheta = dper / minor_r;
+
+    /* minor normal is binormal to major normal and radius */
+    vec3 minor_normal = this->major_normal.cross(this->major_radius).normalize();
+
+    /* quaternion describing rotation of minor vector */
+    quat minor_rot = quat::from_angleaxis(minor_dtheta, minor_normal), minor_crot = minor_rot.conjugate();
+
+    quat major_rot = quat::from_angleaxis(major_dtheta, major_normal), major_crot = major_rot.conjugate();
+
+    vec3 sum = 0;
+
+    quat major_radius = this->major_radius;
+    quat minor_radius = this->major_radius.normalize() * this->minor_r;
+
+    for(scalar theta = 0; theta < this->major_angle; theta += major_dtheta)
+    {
+        vec3 dpar_vec = minor_normal * dpar;
+        vec3 ds = minor_normal.cross(minor_radius).normalize() * dper + dpar_vec;
+        sum += integrand(this->origin + major_radius + minor_radius, ds);
+
+        /* we need to rotate some vectors: first the major radius and
+         * minor normal about the major normal, and then the minor
+         * radius */
+        /* we also need to rotate the minor radius rotation quaternion
+         * about the origin */
+        major_radius = major_rot * major_radius * major_crot;
+        minor_normal = major_rot * minor_normal * major_crot;
+            
+        minor_radius = minor_rot * minor_radius * minor_crot;
+
+        minor_rot = minor_rot * major_rot;
+        minor_crot = minor_rot.conjugate();
+    }
+
+#if 0
+    if(l < len)
+    {
+        dl = len - l;
+        dtheta = dl / r;
+        rot = quat::from_angleaxis(dtheta, normal);
+        crot = rot.conjugate();
+        dp = this->normal * dtheta * pitch / (2 * M_PI);
+
+        vec3 ds = this->normal.cross(radius).normalize() * dl + dp;
+        sum += integrand(this->origin + axis + radius, ds);
+    }
+#endif
+
+    return sum;
+}
+
-- 
cgit v1.1