From c571793267fdbbc7c6229071a3146c18c2c1b489 Mon Sep 17 00:00:00 2001
From: John Honniball <coredump@virginmedia.com>
Date: Sat, 22 Aug 2020 17:25:35 +0100
Subject: [PATCH] Get the 'spiral()' function right. It wasn't doing the right
 number of line segments to give a full 'turn'. TODO: move this function into
 the library, hopefully a correct version.

---
 dala2.c  | 11 +++++------
 dala2c.c | 11 +++++------
 twist.c  |  2 +-
 3 files changed, 11 insertions(+), 13 deletions(-)

diff --git a/dala2.c b/dala2.c
index 80bfd3d..965f7a7 100644
--- a/dala2.c
+++ b/dala2.c
@@ -977,16 +977,15 @@ void superellipse(const double x0, const double y0, const double a, const double
 
 void spiral(const double cx, const double cy, const double radius, const double ang, const int n)
 {
-   double theta = ang;
-   double thinc = 2.0 * M_PI / 72.0;
+   double delta = 2.0 * M_PI / 72.0;
    int i;
-   int ptnumber = 72 * n;
+   int npts = 72 * n;
 
    moveto(cx, cy);
 
-   for (i = 0; i < ptnumber; i++) {
-      theta += thinc;
-      const double r = (radius * i) / (double)ptnumber;
+   for (i = 1; i <= npts; i++) {
+      const double theta = ang + (delta * (double)i);
+      const double r = (radius * i) / (double)npts;
       const double x = (r * cos(theta)) + cx;
       const double y = (r * sin(theta)) + cy;
 
diff --git a/dala2c.c b/dala2c.c
index 1853066..d59e8c8 100644
--- a/dala2c.c
+++ b/dala2c.c
@@ -126,18 +126,17 @@ int main (int argc, char * const argv[])
 
 void spiral (double cx, double cy, double radius, double ang, int n)
 {
-   double theta = ang;
-   double thinc = 2.0 * M_PI / 72.0;
+   double delta = 2.0 * M_PI / 72.0;
    double r;
    int i;
-   int ptnumber = 72 * n;
+   int npts = 72 * n;
    double x, y;
    
    moveto (cx, cy);
    
-   for (i = 0; i < ptnumber; i++) {
-      theta += thinc;
-      r = (radius * i) / (double)ptnumber;
+   for (i = 1; i <= npts; i++) {
+      const double theta = ang + (delta * (double)i);
+      r = (radius * i) / (double)npts;
       x = (r * cos (theta)) + cx;
       y = (r * sin (theta)) + cy;
       
diff --git a/twist.c b/twist.c
index 9508ef4..5cfd156 100644
--- a/twist.c
+++ b/twist.c
@@ -71,7 +71,7 @@ void spiral(const double xc, const double yc, const double r1, const double r2,
    int i;
    const double dr = (r2 - r1) / (72.0 * n);
    
-   for (i = 0; i < (72 * n); i++) {
+   for (i = 0; i <= (72 * n); i++) {
       const double theta = ang + (delta * i);
       const double r = r1 + (dr * i);
       const double x = (r * cos(theta)) + xc;