Code:

// Polar basics demo for the
// FastLED Podcast #2
// https://www.youtube.com/watch?v=KKjFRZFBUrQ
//
// VO.1 preview version
// by Stefan Petrick 2023
// This code is licenced under a
// Creative Commons Attribution
// License CC BY-NC 3.0
#if defined(ARDUINO_TEENSY40) || defined(ARDUINO_TEENSY41)
#include <MatrixHardware_Teensy4_ShieldV5.h> // SmartLED Shield for Teensy 4 (V5)
#elif defined(ARDUINO_TEENSY35) || defined(ARDUINO_TEENSY36)
#include <MatrixHardware_Teensy4_ShieldV4.h> // SmartLED Shield for Teensy 4 (V5)
#else
#error "Include the correct header for the microprocessor"
#endif
#include <SmartMatrix.h>
/* SmartMatrix configuration and memory allocation */
#define COLOR_DEPTH 24 // Choose the color depth used for storing pixels in the layers: 24 or 48
// (24 is good for most sketches - If the sketch uses type `rgb24` directly,
// COLOR_DEPTH must be 24)
#define kMatrixWidth 64U // Set to the width of your display, must be a multiple of 8
#define kMatrixHeight 64U // Set to the height of your display
const uint8_t kRefreshDepth = 36; // Tradeoff of color quality vs refresh rate, max brightness, and RAM usage.
// 36 is typically good, drop down to 24 if you need to.
// On Teensy, multiples of 3, up to 48: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48.
// On ESP32: 24, 36, 48
const uint8_t kDmaBufferRows = 4; // known working: 2-4, use 2 to save RAM, more to keep from dropping frames
// and automatically lowering refresh rate. (This isn't used on ESP32, leave as default)
// Choose the configuration that matches your panels. See more details in
// MatrixCommonHub75.h and the docs: https://github.com/pixelmatix/SmartMatrix/wiki
#if kMatrixHeight == 64
const uint8_t kPanelType = SM_PANELTYPE_HUB75_64ROW_MOD32SCAN;
#elif kMatrixHeight == 32
const uint8_t kPanelType = SM_PANELTYPE_HUB75_32ROW_MOD16SCAN;
#elif kMatrixHeight == 16
const uint8_t kPanelType = SM_PANELTYPE_HUB75_16ROW_MOD8SCAN;
#else
#error "Update setting kPanelType"
#endif
// see docs for options: https://github.com/pixelmatix/SmartMatrix/wiki
const uint32_t kMatrixOptions = (SM_HUB75_OPTIONS_NONE);
const uint8_t kBackgroundLayerOptions = (SM_BACKGROUND_OPTIONS_NONE);
const uint8_t kScrollingLayerOptions = (SM_SCROLLING_OPTIONS_NONE);
SMARTMATRIX_ALLOCATE_BUFFERS(matrix,
kMatrixWidth,
kMatrixHeight,
kRefreshDepth,
kDmaBufferRows,
kPanelType,
kMatrixOptions);
SMARTMATRIX_ALLOCATE_BACKGROUND_LAYER(backgroundLayer,
kMatrixWidth,
kMatrixHeight,
COLOR_DEPTH,
kBackgroundLayerOptions);
// range 0-255
const int defaultBrightness = 255;
const rgb24 COLOR_BLACK = { 0, 0, 0 };
//#include <FastLED.h>
//#include <FLOAT.h>
#define WIDTH kMatrixWidth // how many LEDs are in one row?
#define HEIGHT kMatrixHeight // how many rows?
#define NUM_LEDS ((WIDTH) * (HEIGHT))
float runtime; // elapse ms since startup
float newdist, newangle; // parameters for image reconstruction
float z; // 3rd dimension for the 3d noise function
float offset_x, offset_y; // wanna shift the cartesians during runtime?
float scale_x, scale_y; // cartesian scaling in 2 dimensions
float dist, angle; // the actual polar coordinates
int x, y; // the cartesian coordiantes
int num_x = WIDTH; // horizontal pixel count
int num_y = HEIGHT; // vertical pixel count
// Background for setting the following 2 numbers: the FastLED inoise16() function returns
// raw values ranging from 0-65535. In order to improve contrast we filter this output and
// stretch the remains. In histogram (photography) terms this means setting a blackpoint and
// a whitepoint. low_limit MUST be smaller than high_limit.
uint16_t low_limit = 30000; // everything lower drawns in black
// higher numer = more black & more contrast present
uint16_t high_limit = 50000; // everything higher gets maximum brightness & bleeds out
// lower number = the result will be more bright & shiny
float center_x = (num_x / 2) - 0.5; // the reference point for polar coordinates
float center_y = (num_y / 2) - 0.5; // (can also be outside of the actual xy matrix)
//float center_x = 20; // the reference point for polar coordinates
//float center_y = 20;
//CRGB leds[WIDTH * HEIGHT]; // framebuffer
float theta [WIDTH] [HEIGHT]; // look-up table for all angles
float distance[WIDTH] [HEIGHT]; // look-up table for all distances
float vignette[WIDTH] [HEIGHT];
float inverse_vignette[WIDTH] [HEIGHT];
float spd; // can be used for animation speed manipulation during runtime
float show1, show2, show3, show4, show5; // to save the rendered values of all animation layers
float red, green, blue; // for the final RGB results after the colormapping
float c, d, e, f; // factors for oscillators
float linear_c, linear_d, linear_e, linear_f; // linear offsets
float angle_c, angle_d, angle_e, angle_f; // angle offsets
float noise_angle_c, noise_angle_d, noise_angle_e, noise_angle_f; // angles based on linear noise travel
float dir_c, dir_d, dir_e, dir_f; // direction multiplicators
void setup() {
Serial.begin(115200); // check serial monitor for current fps count
// Initialize Matrix
matrix.addLayer(&backgroundLayer);
matrix.begin();
matrix.setBrightness(defaultBrightness);
backgroundLayer.fillScreen(COLOR_BLACK);
backgroundLayer.swapBuffers();
// Teensy users: make sure to use the hardware SPI pins 11 & 13
// for best performance
//FastLED.addLeds<APA102, 11, 13, BGR, DATA_RATE_MHZ(12)>(leds, NUM_LEDS);
// FastLED.addLeds<NEOPIXEL, 13>(leds, NUM_LEDS);
render_polar_lookup_table(); // precalculate all polar coordinates
// to improve the framerate
render_vignette_table(9.5); // the number is the desired radius in pixel
// WIDTH/2 generates a circle
}
void loop() {
// set speedratios for the offsets & oscillators
spd = 0.05 ;
c = 0.013 ;
d = 0.017 ;
e = 0.2 ;
f = 0.007 ;
calculate_oscillators(); // get linear offsets and oscillators going
// ...and now let's generate a frame
backgroundLayer.fillScreen(COLOR_BLACK);
for (x = 0; x < num_x; x++) {
for (y = 0; y < num_y; y++) {
// pick polar coordinates from look the up table
dist = distance [x] [y];
angle = theta [y] [x];
// Generation of one layer. Explore the parameters and what they do.
scale_x = 10000; // smaller value = zoom in, bigger structures, less detail
scale_y = 10000; // higher = zoom out, more pixelated, more detail
z = 0; // must be >= 0
newangle = angle + angle_c;
newdist = dist;
offset_x = 0; // must be >=0
offset_y = 0; // must be >=0
show1 = render_pixel();
// Colormapping - Assign rendered values to colors
red = show1;
green = 0;
blue = 0;
// Check the final results.
// Discard faulty RGB values & write the valid results into the framebuffer.
write_pixel_to_framebuffer();
}
}
// Bring background layer to the front
backgroundLayer.swapBuffers ();
// BRING IT ON! SHOW WHAT YOU GOT!
//FastLED.show();
// check serial monitor for current performance data
//EVERY_N_MILLIS(500) report_performance();
}
//-----------------------------------------------------------------------------------end main loop --------------------
void calculate_oscillators() {
runtime = millis(); // save elapsed ms since start up
runtime = runtime * spd; // global anaimation speed
linear_c = runtime * c; // some linear rising offsets 0 to max
linear_d = runtime * d;
linear_e = runtime * e;
linear_f = runtime * f;
angle_c = fmodf(linear_c, 2 * PI); // some cyclic angle offsets 0 to 2*PI
angle_d = fmodf(linear_d, 2 * PI);
angle_e = fmodf(linear_e, 2 * PI);
angle_f = fmodf(linear_f, 2 * PI);
dir_c = sinf(angle_c); // some direction oscillators -1 to 1
dir_d = sinf(angle_d);
dir_e = sinf(angle_e);
dir_f = sinf(angle_f);
uint16_t noi;
noi = inoise16(10000 + linear_c * 100000); // some noise controlled angular offsets
noise_angle_c = map_float(noi, 0, 65535 , 0, 4*PI);
noi = inoise16(20000 + linear_d * 100000);
noise_angle_d = map_float(noi, 0, 65535 , 0, 4*PI);
noi = inoise16(30000 + linear_e * 100000);
noise_angle_e = map_float(noi, 0, 65535 , 0, 4*PI);
noi = inoise16(40000 + linear_f * 100000);
noise_angle_f = map_float(noi, 0, 65535 , 0, 4*PI);
}
// given a static polar origin we can precalculate
// all the (expensive) polar coordinates
void render_polar_lookup_table() {
for (int xx = 0; xx < num_x; xx++) {
for (int yy = 0; yy < num_y; yy++) {
float dx = xx - center_x;
float dy = yy - center_y;
distance[xx] [yy] = hypotf(dx, dy);
theta[xx] [yy] = atan2f(dy, dx);
}
}
}
// calculate distance and angle of the point relative to
// the polar origin defined by center_x & center_y
void get_polar_values() {
// calculate current cartesian distances (deltas) from polar origin point
float dx = x - center_x;
float dy = y - center_y;
// calculate distance between current point & polar origin
// (length of the origin vector, pythgorean theroem)
// dist = sqrt((dx*dx)+(dy*dy));
dist = hypotf(dx, dy);
// calculate the angle
// (where around the polar origin is the current point?)
angle = atan2f(dy, dx);
// done, that's all we need
}
// convert polar coordinates back to cartesian
// & render noise value there
float render_pixel() {
// convert polar coordinates back to cartesian ones
float newx = (offset_x + center_x - (cosf(newangle) * newdist)) * scale_x;
float newy = (offset_y + center_y - (sinf(newangle) * newdist)) * scale_y;
// render noisevalue at this new cartesian point
uint16_t raw_noise_field_value = inoise16(newx, newy, z);
// a lot is happening here, namely
// A) enhance histogram (improve contrast) by setting the black and white point
// B) scale the result to a 0-255 range
// it's the contrast boosting & the "colormapping" (technically brightness mapping)
if (raw_noise_field_value < low_limit) raw_noise_field_value = low_limit;
if (raw_noise_field_value > high_limit) raw_noise_field_value = high_limit;
float scaled_noise_value = map_float(raw_noise_field_value, low_limit, high_limit, 0, 255);
return scaled_noise_value;
// done, we've just rendered one color value for one single pixel
}
// float mapping maintaining 32 bit precision
// we keep values with high resolution for potential later usage
float map_float(float x, float in_min, float in_max, float out_min, float out_max) {
float result = (x-in_min) * (out_max-out_min) / (in_max-in_min) + out_min;
if (result < out_min) result = out_min;
if( result > out_max) result = out_max;
return result;
}
// Avoid any possible color flicker by forcing the raw RGB values to be 0-255.
// This enables to play freely with random equations for the colormapping
// without causing flicker by accidentally missing the valid target range.
void rgb_sanity_check() {
// rescue data if possible: when negative return absolute value
if (red < 0) red = abs(red);
if (green < 0) green = abs(green);
if (blue < 0) blue = abs(blue);
// discard everything above the valid 0-255 range
if (red > 255) red = 255;
if (green > 255) green = 255;
if (blue > 255) blue = 255;
}
// check result after colormapping and store the newly rendered rgb data
void write_pixel_to_framebuffer() {
// the final color values shall not exceed 255 (to avoid flickering pixels caused by >255 = black...)
// negative values * -1
rgb_sanity_check();
// write the rendered pixel into the framebutter
//leds[XY(x, y)] = finalcolor;
backgroundLayer.drawPixel(x, y, {(uint8_t)red, (uint8_t)green, (uint8_t)blue});
}
// find the right led index
//uint16_t XY(uint8_t x, uint8_t y) {
// if (y & 1) // check last bit
// return (y + 1) * WIDTH - 1 - x; // reverse every second line for a serpentine lled layout
// else
// return y * WIDTH + x; // use this equation only for a line by line led layout
//} // remove the previous 3 lines of code in this case
// make it look nicer - expand low brightness values and compress high brightness values,
// basically we perform gamma curve bending for all 3 color chanels,
// making more detail visible which otherwise tends to get lost in brightness
void adjust_gamma() {
//for (uint16_t i = 0; i < NUM_LEDS; i++)
//{
// leds[i].r = dim8_video(leds[i].r);
// leds[i].g = dim8_video(leds[i].g);
// leds[i].b = dim8_video(leds[i].b);
//}
}
// precalculate a radial brightness mask
void render_vignette_table(float filter_radius) {
for (int xx = 0; xx < num_x; xx++) {
for (int yy = 0; yy < num_y; yy++) {
vignette[xx] [yy] = (filter_radius - distance[xx] [yy]) / filter_radius;
if (vignette[xx] [yy] < 0) vignette[xx] [yy] = 0;
}
}
}
// show current framerate and rendered pixels per second
void report_performance() {
//int fps = FastLED.getFPS(); // frames per second
//int kpps = (fps * HEIGHT * WIDTH) / 1000; // kilopixel per second
//Serial.print(kpps); Serial.print(" kpps ... ");
//Serial.print(fps); Serial.print(" fps @ ");
//Serial.print(WIDTH*HEIGHT); Serial.println(" LEDs ... ");
}