perfect exponential plots #606

Previously, we had the first interval top out at 1.0. This made
clean mathematical sense, but it meant that we wasted the lowest
|states - 1| representations. We now top out at ibase**(states - 1).
The very bottom representation tops out at 1, meaning that any data
is always distinguishable from no data. We no longer explicitly
print spaces (aka the zeroth state for each glyph clade), so that
we can exhibit more transparency. Properly account for miny at
all times. Slots in an exponential plot are now exponential
throughout; before, it was exponential across rows, and linear
within a row.

src/demo/xray.c

@@ -25,7 +25,6 @@ make_slider(struct notcurses* nc, int dimy){
   channels_set_fg_alpha(&channels, CELL_ALPHA_TRANSPARENT);
   channels_set_bg_alpha(&channels, CELL_ALPHA_TRANSPARENT);
   ncplane_set_base(n, " ", 0, channels);
-  ncplane_set_bg_alpha(n, CELL_ALPHA_BLEND);
   ncplane_set_scrolling(n, true);
   int r = 0x5f;
   int g = 0xaf;

src/input/input.cpp

@@ -215,6 +215,7 @@ int main(void){
   auto n = nc.get_stdplane(&dimy, &dimx);
   ncpp::Plane pplane{PLOTHEIGHT, dimx, dimy - PLOTHEIGHT,  0, nullptr};
   struct ncplot_options popts{};
+  // FIXME would be nice to switch over to exponential at some level
   popts.flags = NCPLOT_OPTIONS_LABELTICKSD;
   popts.minchannel = popts.maxchannel = 0;
   channels_set_fg_rgb(&popts.minchannel, 0x40, 0x50, 0xb0);

src/lib/plot.h

@@ -129,12 +129,13 @@ class ncppplot {
    // each transition is worth this much change in value
    const size_t states = geomdata[gridtype].height;
    // FIXME can we not rid ourselves of this meddlesome double? either way, the
-   // interval is one row's range (for linear plots), or the log10 of each row's
-   // range (for exponential plots).
+   // interval is one row's range (for linear plots), or the base (base^slots==
+   // maxy-miny) of the range (for exponential plots).
    double interval;
    if(exponentiali){
      if(maxy > miny){
-       interval = pow(maxy - miny, (double)1 / ((dimy - 1) * states));
+       interval = pow(maxy - miny, (double)1 / (dimy * states));
+//fprintf(stderr, "miny: %ju maxy: %ju dimy: %d states: %zu\n", miny, maxy, dimy, states);
      }else{
        interval = 0;
      }
@@ -150,7 +151,7 @@ class ncppplot {
      for(int y = 0 ; y < dimy ; ++y){
        char buf[PREFIXSTRLEN + 1];
        if(exponentiali){
-         ncmetric(pow(interval, y * states) * 100, 100, buf, 0, 1000, '\0');
+         ncmetric(pow(interval, y * states + (states - 1)) * 100, 100, buf, 0, 1000, '\0');
        }else{
          ncmetric(interval * states * (y + 1) * 100, 100, buf, 0, 1000, '\0');
        }
@@ -187,7 +188,7 @@ class ncppplot {
      double intervalbase = miny;
      const wchar_t* egc = geomdata[gridtype].egcs;
      for(int y = 0 ; y < dimy ; ++y){
-       size_t egcidx, sumidx = 0;
+       size_t egcidx = 0, sumidx = 0;
        // if we've got at least one interval's worth on the number of positions
        // times the number of intervals per position plus the starting offset,
        // we're going to print *something*
@@ -196,11 +197,15 @@ class ncppplot {
          sumidx *= states;
          if(intervalbase < gvals[i]){
            if(exponentiali){
-             egcidx = (log(gvals[i]) - log(intervalbase)) * states / interval;
+             // we want the log-base-interval of gvals[i]
+             double scaled = log(gvals[i] - miny) / log(interval);
+             double sival = intervalbase ? log(intervalbase) / log(interval) : 0;
+             egcidx = scaled - sival;
+//fprintf(stderr, "egcidx: %zu gvals: %u interval: %f scaled: %f sival: %f\n", egcidx, gvals[i], interval, scaled, sival);
            }else{
              egcidx = (gvals[i] - intervalbase) / interval;
            }
-//fprintf(stderr, "%d/%d ibase: %f egcidx: %zu\n", dimy - y - 1, x, intervalbase, egcidx);
+//fprintf(stderr, "%d/%d ibase: %f ival: %f egcidx: %zu\n", dimy - y - 1, x, intervalbase, interval, egcidx);
            if(egcidx >= states){
              egcidx = states - 1;
              done = false;
@@ -210,14 +215,16 @@ class ncppplot {
            egcidx = 0;
          }
        }
-       if(ncplane_putwc_yx(ncp, dimy - y - 1, x, egc[sumidx]) <= 0){
-         return -1;
+       if(sumidx){
+         if(ncplane_putwc_yx(ncp, dimy - y - 1, x, egc[sumidx]) <= 0){
+           return -1;
+         }
        }
        if(done){
          break;
        }
        if(exponentiali){
-         intervalbase = miny + pow(interval, y * states);
+         intervalbase = miny + pow(interval, (y + 1) * states - 1);
        }else{
          intervalbase += (states * interval);
        }