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DisplayGDEW075T7.cpp
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DisplayGDEW075T7.cpp
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/**
* Display class supporting 4-level greyscale for GDEW075T7 e-paper display, aka the 800x480 7.5" B/W from Waveshare.
*
* https://www.good-display.com/product/244.html
*
* Datasheet (for a different display controller) that has the LUT commands documented:
* https://www.smart-prototyping.com/image/data/9_Modules/EinkDisplay/GDEW0154T8/IL0373.pdf
*/
#include <Arduino.h>
#include <stdlib.h>
#include "DisplayGDEW075T7.h"
// Display commands
const uint8_t CMD_PSR = 0x00;
const uint8_t CMD_PWR = 0x01;
const uint8_t CMD_POWEROFF = 0x02;
const uint8_t CMD_POWERON = 0x04;
const uint8_t CMD_BTST = 0x06;
const uint8_t CMD_DEEPSLEEP = 0x07;
const uint8_t CHK_DEEPSLEEP = 0xA5;
const uint8_t CMD_DTM1 = 0x10;
const uint8_t CMD_REFRESH = 0x12;
const uint8_t CMD_DSP = 0x11;
const uint8_t CMD_DTM2 = 0x13;
const uint8_t CMD_DUAL_SPI = 0x15;
const uint8_t CMD_SET_LUTVCOM = 0x20;
const uint8_t CMD_SET_LUTWW = 0x21;
const uint8_t CMD_SET_LUTBW = 0x22;
const uint8_t CMD_SET_LUTWB = 0x23;
const uint8_t CMD_SET_LUTBB = 0x24;
const uint8_t CMD_SET_LUTBD = 0x25;
const uint8_t CMD_PLL = 0x30;
const uint8_t CMD_VCOM_CDI = 0x50;
const uint8_t CMD_TCON = 0x60;
const uint8_t CMD_TRES = 0x61;
const uint8_t CMD_GSST = 0x65;
const uint8_t CMD_FLG = 0x71;
const uint8_t CMD_VDCS = 0x82;
// Supported LUT voltage levels
#define LEVEL_GND 0b00
#define LEVEL_VDH 0b01
#define LEVEL_VDL 0b10
#define LEVEL_VDHR 0b11
#define LEVEL_VCOM_VCMDC 0b00
#define LEVEL_VCOM_FLOAT 0b11
/**
* Macro to generate an LUT row while preserving some readability.
*
* l* params are the voltages to apply at each step, and t* are the number of frames to keep that voltage applied.
* r is the number of times the enitre sequence is to be repeated.
*/
#define LUT_ROW(l0, t0, l1, t1, l2, t2, l3, t3, r) (l0 << 6) | (l1 << 4) | (l2 << 2) | l3, t0, t1, t2, t3, r
#define LUT_ROW_NOOP LUT_ROW(0, 0, 0, 0, 0, 0, 0, 0, 0)
/**
* These LUTs are the original ones provided for this display by Waveshare.
*
* Currently not used, but kept here for reference.
*
* https://github.com/waveshare/e-Paper/blob/master/Arduino/epd7in5_V2/epd7in5_V2.cpp
*/
const uint8_t LUT_VCOM_1BIT[] = {
LUT_ROW(LEVEL_VCOM_VCMDC, 15, LEVEL_VCOM_VCMDC, 15, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VCOM_VCMDC, 15, LEVEL_VCOM_VCMDC, 1, LEVEL_VCOM_VCMDC, 15, LEVEL_VCOM_VCMDC, 1, 2),
LUT_ROW(LEVEL_VCOM_VCMDC, 15, LEVEL_VCOM_VCMDC, 15, 0, 0, 0, 0, 1),
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
};
const uint8_t LUT_WW_1BIT[] = {
LUT_ROW(LEVEL_GND, 15, LEVEL_VDH, 15, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDL, 15, LEVEL_GND, 1, LEVEL_VDH, 15, LEVEL_GND, 1, 2),
LUT_ROW(LEVEL_GND, 15, LEVEL_VDL, 15, 0, 0, 0, 0, 1),
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
};
const uint8_t LUT_BW_1BIT[] = {
LUT_ROW(LEVEL_GND, 15, LEVEL_VDH, 15, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDL, 15, LEVEL_GND, 1, LEVEL_VDH, 15, LEVEL_GND, 1, 2),
LUT_ROW(LEVEL_GND, 15, LEVEL_VDL, 15, 0, 0, 0, 0, 1),
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
};
const uint8_t LUT_WB_1BIT[] = {
LUT_ROW(LEVEL_VDL, 15, LEVEL_GND, 15, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDL, 15, LEVEL_GND, 1, LEVEL_VDH, 15, LEVEL_GND, 1, 2),
LUT_ROW(LEVEL_VDH, 15, LEVEL_GND, 15, 0, 0, 0, 0, 1),
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
};
const uint8_t LUT_BB_1BIT[] = {
LUT_ROW(LEVEL_VDL, 15, LEVEL_GND, 15, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDL, 15, LEVEL_GND, 1, LEVEL_VDH, 15, LEVEL_GND, 1, 2),
LUT_ROW(LEVEL_VDH, 15, LEVEL_GND, 15, 0, 0, 0, 0, 1),
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
};
/**
* These LUTs are from the GxEPD2 project, they enable support for 4 color greyscale.
* The author of that project says these waveforms are provided by GoodDisplay, however
* they aren't meant for this particular display and may have varying results between displays,
* although they look perfect on the one I have.
*
* The only modification I've made is repeating the 2nd waveform twice to reduce ghosting.
* I don't forsee this having any negative effects since that waveform is balanced between VDH/VDL.
* Ghosting seems to increase as temperature decreases, which makes sense because the oil in the display
* will be more viscous. Increasing R2 will help reduce ghosting more at low temperatures at the cost of
* increated refresh time.
*
* https://github.com/ZinggJM/GxEPD2_4G/blob/master/src/epd/GxEPD2_750_T7.cpp
*/
#define T1 10
#define T2 20
#define R2 2
#define T3_1 20
#define T3_2 10
const uint8_t LUT_VCOM_2BIT[] = {
LUT_ROW(LEVEL_VCOM_VCMDC, T1, 0, 0, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDH, T2, LEVEL_VDL, T2, 0, 0, 0, 0, R2),
LUT_ROW(LEVEL_VCOM_VCMDC, T3_1, 0, 0, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VCOM_VCMDC, 19, LEVEL_VCOM_VCMDC, 10, LEVEL_VCOM_VCMDC, 1, 0, 0, 1),
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
};
const uint8_t LUT_WHITE_2BIT[] = {
LUT_ROW(LEVEL_VDH, T1, 0, 0, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDL, T2, LEVEL_VDH, T2, 0, 0, 0, 0, R2),
LUT_ROW(LEVEL_GND, T3_1, LEVEL_VDH, T3_2, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDL, 19, LEVEL_VDL, 1, 0, 0, 0, 0, 1),
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
};
const uint8_t LUT_DGREY_2BIT[] = {
LUT_ROW(LEVEL_VDH, T1, 0, 0, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDL, T2, LEVEL_VDH, T2, 0, 0, 0, 0, R2),
LUT_ROW(LEVEL_GND, T3_1, LEVEL_GND, T3_2, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDL, 12, LEVEL_VDH, 1, LEVEL_VDL, 3, LEVEL_VDH, 4, 1),
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
};
const uint8_t LUT_LGREY_2BIT[] = {
LUT_ROW(LEVEL_VDH, T1, 0, 0, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDL, T2, LEVEL_VDH, T2, 0, 0, 0, 0, R2),
LUT_ROW(LEVEL_GND, T3_1, LEVEL_GND, T3_2, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDL, 11, LEVEL_VDH, 4, LEVEL_VDL, 4, LEVEL_VDH, 1, 1),
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
};
const uint8_t LUT_BLACK_2BIT[] = {
LUT_ROW(LEVEL_VDL, T1, 0, 0, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDL, T2, LEVEL_VDH, T2, 0, 0, 0, 0, R2),
LUT_ROW(LEVEL_GND, T3_1, LEVEL_VDL, T3_2, 0, 0, 0, 0, 1),
LUT_ROW(LEVEL_VDH, 19, LEVEL_VDH, 1, 0, 0, 0, 0, 1),
LUT_ROW_NOOP,
LUT_ROW_NOOP,
LUT_ROW_NOOP,
};
/**
* These aren't waveform LUTs, they map 2-bit color values to the old (DTM1) and new (DTM2)
* data values sent to the display.
*/
const uint8_t LUT_DTM1[] = {
/* WHITE */ 0,
/* LGREY */ 0,
/* DGREY */ 1,
/* BLACK */ 1,
};
const uint8_t LUT_DTM2[] = {
/* WHITE */ 0,
/* LGREY */ 1,
/* DGREY */ 0,
/* BLACK */ 1,
};
#define BUSY_TIMEOUT 5000
DisplayGDEW075T7::~DisplayGDEW075T7() {
_spi->endTransaction();
_spi->end();
delete _spi;
delete[] _frameBuffer;
};
DisplayGDEW075T7::DisplayGDEW075T7(uint8_t spi_bus, uint8_t cs_pin, uint8_t reset_pin, uint8_t dc_pin, uint8_t busy_pin)
{
_spiBus = spi_bus;
_resetPin = reset_pin;
_dcPin = dc_pin;
_csPin = cs_pin;
_busyPin = busy_pin;
pinMode(_csPin, OUTPUT);
pinMode(_resetPin, OUTPUT);
pinMode(_dcPin, OUTPUT);
pinMode(_busyPin, INPUT);
_spi = new SPIClass(_spiBus);
_spi->begin();
_spi->beginTransaction(SPISettings(7000000, MSBFIRST, SPI_MODE0));
_frameBuffer = new uint8_t[FRAMEBUFFER_LENGTH];
setRotation(ROTATION_0);
setAlpha(NO_ALPHA);
clear();
};
void DisplayGDEW075T7::wakeup()
{
digitalWrite(_resetPin, HIGH);
delay(20);
digitalWrite(_resetPin, LOW);
delay(4);
digitalWrite(_resetPin, HIGH);
delay(20);
digitalWrite(_csPin, LOW);
// Most of this is Waveshare's defaults
sendCommand(CMD_PWR); // power setting
sendData(0x17); // BD_EN=1, VSR_EN=1, VS_EN=1, VG_EN=1, waveshare
sendData(0x17); // VPP_EN=0, VCOM_SLEW=1, VGH=20v, VGL=-20v
sendData(0x3F); // VDH=15v
sendData(0x3F); // VDL=-15v
sendData(0x11); // VDHR=5.8v
sendCommand(CMD_VDCS); // VCOM DC Setting (min 0x00 = -0.1v, max 0x4F = -4.05v)
sendData(0x26); // -2.0v
sendCommand(CMD_BTST); // Booster Setting
sendData(0x27);
sendData(0x27);
sendData(0x2F);
sendData(0x17);
sendCommand(CMD_PLL);
sendData(0x06); // 150hz
sendCommand(CMD_POWERON);
delay(100);
waitUntilIdle();
sendCommand(CMD_PSR); // PANNEL SETTING
sendData(0x3F); // Custom LUT, KW mode, UD=1, SHL=1, SHD_N=1, RST_N=1
sendCommand(CMD_TRES);
sendData(NATIVE_WIDTH / 256);
sendData(NATIVE_WIDTH % 256);
sendData(NATIVE_HEIGHT / 256);
sendData(NATIVE_HEIGHT % 256);
sendCommand(CMD_DUAL_SPI);
sendData(0x00);
sendCommand(CMD_VCOM_CDI); // VCOM AND DATA INTERVAL SETTING
sendData(0x00); // BDZ=0, BDV=00, N2OCP=0, DDX=00
// sendData(0x00); // CDI=17
sendData(0x07); // CDI=10
sendCommand(CMD_TCON); // TCON SETTING
sendData(0x22);
sendCommand(CMD_GSST); // Resolution setting
sendData(0x00);
sendData(0x00);
sendData(0x00);
sendData(0x00);
setLut(CMD_SET_LUTVCOM, LUT_VCOM_2BIT);
setLut(CMD_SET_LUTWW, LUT_WHITE_2BIT);
setLut(CMD_SET_LUTBW, LUT_DGREY_2BIT);
setLut(CMD_SET_LUTWB, LUT_LGREY_2BIT);
setLut(CMD_SET_LUTBB, LUT_BLACK_2BIT);
setLut(CMD_SET_LUTBD, LUT_WHITE_2BIT);
}
void DisplayGDEW075T7::sendCommand(uint8_t command)
{
digitalWrite(_dcPin, LOW);
_spi->transfer(command);
digitalWrite(_dcPin, HIGH);
}
void DisplayGDEW075T7::sendData(uint8_t data)
{
_spi->transfer(data);
}
void DisplayGDEW075T7::waitUntilIdle()
{
unsigned long start = millis();
do {
delay(5);
} while (digitalRead(_busyPin) == LOW && millis() - start < BUSY_TIMEOUT);
delay(20);
}
void DisplayGDEW075T7::setLut(uint8_t cmd, const uint8_t* lut)
{
sendCommand(cmd);
for (size_t i = 0; i < 42; ++i) {
sendData(lut[i]);
}
}
void DisplayGDEW075T7::refresh()
{
wakeup();
uint32_t i, j;
uint16_t chunk; // Holds 8px of frame_buffer
uint8_t data; // Holds 8px of display output
sendCommand(CMD_DTM1);
for (i = 0; i < FRAMEBUFFER_LENGTH; i += 2) {
data = 0;
chunk = (_frameBuffer[i] << 8) | _frameBuffer[i + 1];
for (uint8_t j = 0; j < 8; ++j) {
data |= LUT_DTM1[(chunk >> (j * 2)) & 0b11] << j;
}
sendData(data);
}
sendCommand(CMD_DTM2);
for (i = 0; i < FRAMEBUFFER_LENGTH; i += 2) {
data = 0;
chunk = (_frameBuffer[i] << 8) | _frameBuffer[i + 1];
for (uint8_t j = 0; j < 8; ++j) {
data |= LUT_DTM2[(chunk >> (j * 2)) & 0b11] << j;
}
sendData(data);
}
sendCommand(CMD_REFRESH);
delay(100);
waitUntilIdle();
sleep();
}
void DisplayGDEW075T7::sleep()
{
sendCommand(CMD_POWEROFF);
waitUntilIdle();
sendCommand(CMD_DEEPSLEEP);
sendData(CHK_DEEPSLEEP);
digitalWrite(_csPin, HIGH);
}
void DisplayGDEW075T7::clear(uint8_t color)
{
memset(_frameBuffer, (color << 6) | (color << 4) | (color << 2) | color, FRAMEBUFFER_LENGTH);
}
void DisplayGDEW075T7::test()
{
memset(
_frameBuffer,
(BLACK << 6) | (BLACK << 4) | (BLACK << 2) | BLACK,
FRAMEBUFFER_LENGTH / 4
);
memset(
&_frameBuffer[FRAMEBUFFER_LENGTH / 4],
(DGREY << 6) | (DGREY << 4) | (DGREY << 2) | DGREY,
FRAMEBUFFER_LENGTH / 4
);
memset(
&_frameBuffer[FRAMEBUFFER_LENGTH / 2],
(LGREY << 6) | (LGREY << 4) | (LGREY << 2) | LGREY,
FRAMEBUFFER_LENGTH / 4
);
memset(
&_frameBuffer[FRAMEBUFFER_LENGTH * 3 / 4],
(WHITE << 6) | (WHITE << 4) | (WHITE << 2) | WHITE,
FRAMEBUFFER_LENGTH / 4
);
}
size_t DisplayGDEW075T7::getPixelIndex(int32_t x, int32_t y)
{
if (x < 0 || x > _width || y < 0 || y > _height) {
return SIZE_MAX;
}
switch (_rotation) {
case ROTATION_90:
std::swap(x, y);
x = NATIVE_WIDTH - 1 - x;
break;
case ROTATION_180:
x = NATIVE_WIDTH - 1 - x;
y = NATIVE_HEIGHT - 1 - y;
break;
case ROTATION_270:
std::swap(x, y);
y = NATIVE_HEIGHT - 1 - y;
break;
default:
break;
}
return NATIVE_WIDTH * y + x;
}
uint8_t DisplayGDEW075T7::getPx(int32_t x, int32_t y)
{
const uint32_t i = getPixelIndex(x, y);
if (i != SIZE_MAX) {
return (_frameBuffer[i / 4] >> ((3 - i % 4) * 2)) & 0b11;
} else {
return 0;
}
}
void DisplayGDEW075T7::setPx(int32_t x, int32_t y, uint8_t color)
{
const uint32_t i = getPixelIndex(x, y);
if (i != SIZE_MAX) {
uint8_t *fb = &_frameBuffer[i / 4];
const uint8_t shift = (3 - i % 4) * 2;
*fb &= ~(0b11 << shift);
*fb |= (color & 0b11) << shift;
}
}
void DisplayGDEW075T7::drawImage(const Image &image, int32_t x, int32_t y, Align align)
{
adjustAlignment(&x, &y, image.width, image.height, align);
uint32_t i = 0;
uint8_t color;
for (uint32_t y_src = 0; y_src < image.height; ++y_src) {
for (uint32_t x_src = 0; x_src < image.width; ++x_src, ++i) {
color = (image.data[i / 4] >> ((3 - i % 4) * 2)) & 0b11;
if (color != _alpha) {
setPx(x + x_src, y + y_src, color);
}
}
}
}
uint32_t DisplayGDEW075T7::measureText(String str, const Font &font, int32_t tracking)
{
if (str.length() == 0) {
return 0;
}
uint32_t length = 0;
for (char c : str) {
if (c == ' ' || c < font.rangeStart || c > font.rangeEnd) {
length += font.spaceWidth;
} else {
const FontGlyph glyph = font.glyphs[c - font.rangeStart];
length += glyph.width + glyph.left;
}
}
return length + tracking * (str.length() - 1);
}
void DisplayGDEW075T7::drawText(String str, const Font &font, int32_t x, int32_t y, Align align, int32_t tracking)
{
if (align != TOP_LEFT) {
uint32_t width;
// Measurement isn't needed and width isn't used by adjustAligment if horizontal alignment is left
if (!(align & _ALIGN_LEFT)) {
width = measureText(str, font);
}
adjustAlignment(&x, &y, width, font.ascent + font.descent, align);
}
for (char c : str) {
if (c == ' ' || c < font.rangeStart || c > font.rangeEnd) {
x += font.spaceWidth + tracking;
} else {
const FontGlyph glyph = font.glyphs[c - font.rangeStart];
x += glyph.left;
drawImage({ width: glyph.width, height: glyph.height, data: glyph.data }, x, y + glyph.top);
x += glyph.width + tracking;
}
}
}
void DisplayGDEW075T7::drawMultilineText(
std::initializer_list<String> lines,
const Font &font,
int32_t x,
int32_t y,
Align align,
int32_t tracking,
int32_t leading
) {
// This implementation is simple because it assumes justification equals the horizontal alignment,
// and that's all I needed it to do.
leading += font.ascent + font.descent;
if (!(align & _ALIGN_TOP)) {
adjustAlignment(&x, &y, 0, leading * lines.size(), align);
}
// Use top alignment for each line since that axis has already been adjusted for the whole block
align = (Align)(align & ~_ALIGN_BOTTOM & ~_ALIGN_VCENTER | _ALIGN_TOP);
for (String str : lines) {
drawText(str, font, x, y, align, tracking);
y += leading;
}
}
void DisplayGDEW075T7::drawHLine(int32_t x, int32_t y, int32_t length, uint32_t thickness, uint8_t color, Align align)
{
if (length < 0) {
x += length;
length = -length;
}
adjustAlignment(&x, &y, length, thickness, align);
const int32_t ymax = y + thickness;
int32_t i, y1;
for (i = 0; i < length; ++i) {
for (y1 = y; y1 < ymax; ++y1) {
setPx(x + i, y1, color);
}
}
}
void DisplayGDEW075T7::drawVLine(int32_t x, int32_t y, int32_t length, uint32_t thickness, uint8_t color, Align align)
{
if (length < 0) {
y += length;
length = -length;
}
adjustAlignment(&x, &y, thickness, length, align);
const int32_t xmax = x + thickness;
int32_t i, x1;
for (i = 0; i < length; ++i) {
for (x1 = x; x1 < xmax; ++x1) {
setPx(x1, y + i, color);
}
}
}
void DisplayGDEW075T7::fillRect(int32_t x, int32_t y, int32_t width, int32_t height, uint8_t color, Align align)
{
if (width < 0) {
x += width;
width = -width;
}
if (height < 0) {
y += height;
height = -height;
}
adjustAlignment(&x, &y, width, height, align);
int32_t x2 = x + width, y2 = y + height;
for (int xi = x; xi < x2; ++xi) {
for (int yi = y; yi < y2; ++yi) {
setPx(xi, yi, color);
}
}
}
void DisplayGDEW075T7::strokeRect(int32_t x, int32_t y, int32_t width, int32_t height, uint32_t strokeWidth, uint8_t color, bool strokeOutside, Align align)
{
if (width < 0) {
x += width;
width = -width;
}
if (height < 0) {
y += height;
height = -height;
}
adjustAlignment(&x, &y, width, height, align);
if (strokeOutside) {
x -= strokeWidth;
y -= strokeWidth;
width += strokeWidth * 2;
height += strokeWidth * 2;
}
drawHLine(x, y, width, strokeWidth, color, TOP_LEFT);
drawVLine(x, y, height, strokeWidth, color, TOP_LEFT);
drawHLine(x, y + height, width, strokeWidth, color, BOTTOM_LEFT);
drawVLine(x + width, y, height, strokeWidth, color, TOP_RIGHT);
}
void DisplayGDEW075T7::adjustAlignment(int32_t *x, int32_t *y, int32_t width, int32_t height, Align align)
{
if (align & _ALIGN_HCENTER) {
*x -= width / 2;
} else if (align & _ALIGN_RIGHT) {
*x -= width;
}
if (align & _ALIGN_VCENTER) {
*y -= height / 2;
} else if (align & _ALIGN_BOTTOM) {
*y -= height;
}
}
uint32_t DisplayGDEW075T7::getWidth()
{
return _width;
}
uint32_t DisplayGDEW075T7::getHeight()
{
return _height;
}
DisplayGDEW075T7::Rotation DisplayGDEW075T7::getRotation()
{
return _rotation;
}
void DisplayGDEW075T7::setRotation(Rotation rotation)
{
_rotation = rotation;
if (rotation == ROTATION_0 || rotation == ROTATION_180) {
_width = NATIVE_WIDTH;
_height = NATIVE_HEIGHT;
} else {
_width = NATIVE_HEIGHT;
_height = NATIVE_WIDTH;
}
}
uint8_t DisplayGDEW075T7::getAlpha()
{
return _alpha;
}
void DisplayGDEW075T7::setAlpha(uint8_t alpha)
{
_alpha = alpha;
}