With the provision of an extra hint to the CRT and, finally, the realisation about why my scans weren't exactly joining up, improved output precision.

Machines/Atari2600/Atari2600.cpp

@@ -24,7 +24,7 @@ Machine::Machine() :
 	_piaDataValue{0xff, 0xff},
 	_tiaInputValue{0xff, 0xff}
 {
-	_crt = new Outputs::CRT(228, Outputs::CRT::DisplayType::NTSC60, 1, 2);
+	_crt = new Outputs::CRT(228, 1, Outputs::CRT::DisplayType::NTSC60, 1, 2);
 	_crt->set_composite_sampling_function(
 		"float sample(vec2 coordinate, float phase)\n"
 		"{\n"

Machines/Electron/Electron.cpp

@@ -32,7 +32,7 @@ Machine::Machine() :
 	_audioOutputPositionError(0),
 	_currentOutputLine(0),
 	_is_odd_field(false),
-	_crt(std::unique_ptr<Outputs::CRT>(new Outputs::CRT(crt_cycles_per_line, Outputs::CRT::DisplayType::PAL50, 1, 1)))
+	_crt(std::unique_ptr<Outputs::CRT>(new Outputs::CRT(crt_cycles_per_line, 8, Outputs::CRT::DisplayType::PAL50, 1, 1)))
 {
 	_crt->set_rgb_sampling_function(
 		"vec3 rgb_sample(vec2 coordinate)"

Outputs/CRT/CRT.cpp

@@ -43,7 +43,8 @@ void CRT::set_new_timing(unsigned int cycles_per_line, unsigned int height_of_di
 	_vertical_flywheel		= std::unique_ptr<Outputs::Flywheel>(new Outputs::Flywheel(_cycles_per_line * height_of_display, scanlinesVerticalRetraceTime * _cycles_per_line));
 
 	// figure out the divisor necessary to get the horizontal flywheel into a 16-bit range
-	_vertical_flywheel_output_divider = (uint16_t)ceilf(_vertical_flywheel->get_scan_period() / 65536.0f);
+	unsigned int real_clock_scan_period = (_cycles_per_line * height_of_display) / (_time_multiplier * _common_output_divisor);
+	_vertical_flywheel_output_divider = (uint16_t)(ceilf(real_clock_scan_period / 65536.0f) * (_time_multiplier * _common_output_divisor));
 }
 
 void CRT::set_new_display_type(unsigned int cycles_per_line, DisplayType displayType)
@@ -74,14 +75,15 @@ void CRT::allocate_buffers(unsigned int number, va_list sizes)
 	va_end(va);
 }
 
-CRT::CRT() :
+CRT::CRT(unsigned int common_output_divisor) :
 	_next_scan(0),
 	_run_write_pointer(0),
 	_sync_capacitor_charge_level(0),
 	_is_receiving_sync(false),
 	_output_mutex(new std::mutex),
 	_visible_area(Rect(0, 0, 1, 1)),
-	_sync_period(0)
+	_sync_period(0),
+	_common_output_divisor(common_output_divisor)
 {
 	construct_openGL();
 }
@@ -96,7 +98,7 @@ CRT::~CRT()
 	destruct_openGL();
 }
 
-CRT::CRT(unsigned int cycles_per_line, unsigned int height_of_display, ColourSpace colour_space, unsigned int colour_cycle_numerator, unsigned int colour_cycle_denominator, unsigned int number_of_buffers, ...) : CRT()
+CRT::CRT(unsigned int cycles_per_line, unsigned int common_output_divisor, unsigned int height_of_display, ColourSpace colour_space, unsigned int colour_cycle_numerator, unsigned int colour_cycle_denominator, unsigned int number_of_buffers, ...) : CRT(common_output_divisor)
 {
 	set_new_timing(cycles_per_line, height_of_display, colour_space, colour_cycle_numerator, colour_cycle_denominator);
 
@@ -106,7 +108,7 @@ CRT::CRT(unsigned int cycles_per_line, unsigned int height_of_display, ColourSpa
 	va_end(buffer_sizes);
 }
 
-CRT::CRT(unsigned int cycles_per_line, DisplayType displayType, unsigned int number_of_buffers, ...) : CRT()
+CRT::CRT(unsigned int cycles_per_line, unsigned int common_output_divisor, DisplayType displayType, unsigned int number_of_buffers, ...) : CRT(common_output_divisor)
 {
 	set_new_display_type(cycles_per_line, displayType);
 

Outputs/CRT/CRT.hpp

@@ -59,6 +59,11 @@ class CRT {
 			@param cycles_per_line The clock rate at which this CRT will be driven, specified as the number
 			of cycles expected to take up one whole scanline of the display.
 			
+			@param common_output_divisor The greatest a priori common divisor of all cycle counts that will be
+			supplied to @c output_sync, @c output_data, etc; supply 1 if no greater divisor is known. For many
+			machines output will run at a fixed multiple of the clock rate; knowing this divisor can improve
+			internal precision.
+
 			@param height_of_dispaly The number of lines that nominally form one field of the display, rounded
 			up to the next whole integer.
 
@@ -79,7 +84,7 @@ class CRT {
 
 			@see @c set_rgb_sampling_function , @c set_composite_sampling_function
 		*/
-		CRT(unsigned int cycles_per_line, unsigned int height_of_display, ColourSpace colour_space, unsigned int colour_cycle_numerator, unsigned int colour_cycle_denominator, unsigned int number_of_buffers, ...);
+		CRT(unsigned int cycles_per_line, unsigned int common_output_divisor, unsigned int height_of_display, ColourSpace colour_space, unsigned int colour_cycle_numerator, unsigned int colour_cycle_denominator, unsigned int number_of_buffers, ...);
 
 		/*!	Constructs the CRT with the specified clock rate, with the display height and colour
 			subcarrier frequency dictated by a standard display type and with the requested number of
@@ -88,7 +93,7 @@ class CRT {
 			Exactly identical to calling the designated constructor with colour subcarrier information
 			looked up by display type.
 		*/
-		CRT(unsigned int cycles_per_line, DisplayType displayType, unsigned int number_of_buffers, ...);
+		CRT(unsigned int cycles_per_line, unsigned int common_output_divisor, DisplayType displayType, unsigned int number_of_buffers, ...);
 
 		/*!	Resets the CRT with new timing information. The CRT then continues as though the new timing had
 			been provided at construction. */
@@ -232,12 +237,13 @@ class CRT {
 #endif
 
 	private:
-		CRT();
+		CRT(unsigned int common_output_divisor);
 		void allocate_buffers(unsigned int number, va_list sizes);
 
 		// the incoming clock lengths will be multiplied by something to give at least 1000
 		// sample points per line
 		unsigned int _time_multiplier;
+		const unsigned int _common_output_divisor;
 
 		// fundamental creator-specified properties
 		unsigned int _cycles_per_line;

Outputs/CRT/CRTOpenGL.cpp

@@ -375,9 +375,10 @@ void CRT::prepare_shader()
 	glUniform2f(positionConversionUniform, _horizontal_flywheel->get_scan_period(), _vertical_flywheel->get_scan_period() / (unsigned int)_vertical_flywheel_output_divider);
 
 	float scan_angle = atan2f(1.0f / (float)_height_of_display, 1.0f);
-	float scan_normal[] = { sinf(scan_angle), cosf(scan_angle)};
+	float scan_normal[] = { sinf(scan_angle), -cosf(scan_angle)};
-	scan_normal[0] /= (float)_height_of_display;
+	float multiplier = (float)_horizontal_flywheel->get_standard_period() / ((float)_height_of_display * (float)_horizontal_flywheel->get_scan_period());
-	scan_normal[1] /= (float)_height_of_display;
+	scan_normal[0] *= multiplier;
+	scan_normal[1] *= multiplier;
 	glUniform2f(scanNormalUniform, scan_normal[0], scan_normal[1]);
 }
 

Outputs/CRT/Flywheel.hpp

@@ -160,13 +160,21 @@ struct Flywheel
 	}
 
 	/*!
-		@returns the expected length of the scan period.
+		@returns the expected length of the scan period (excluding retrace).
 	*/
 	inline unsigned int get_scan_period()
 	{
 		return _standard_period - _retrace_time;
 	}
 
+	/*!
+		@returns the expected length of a complete scan and retrace cycle.
+	*/
+	inline unsigned int get_standard_period()
+	{
+		return _standard_period;
+	}
+
 	/*!
 		@returns the number of synchronisation events that have seemed surprising since the last time this method was called;
 		a low number indicates good synchronisation.