use crate::bounding_box::BoundingBox; use fnv::FnvHashMap; use smallvec::SmallVec; use std::num::NonZeroU32; use swf::{CharacterId, FillStyle, LineStyle, Matrix, Shape, ShapeRecord, Twips}; pub fn calculate_shape_bounds(shape_records: &[swf::ShapeRecord]) -> swf::Rectangle { let mut bounds = swf::Rectangle { x_min: Twips::new(std::i32::MAX), y_min: Twips::new(std::i32::MAX), x_max: Twips::new(std::i32::MIN), y_max: Twips::new(std::i32::MIN), }; let mut x = Twips::new(0); let mut y = Twips::new(0); for record in shape_records { match record { swf::ShapeRecord::StyleChange(style_change) => { if let Some((move_x, move_y)) = style_change.move_to { x = move_x; y = move_y; bounds.x_min = Twips::min(bounds.x_min, x); bounds.x_max = Twips::max(bounds.x_max, x); bounds.y_min = Twips::min(bounds.y_min, y); bounds.y_max = Twips::max(bounds.y_max, y); } } swf::ShapeRecord::StraightEdge { delta_x, delta_y } => { x += *delta_x; y += *delta_y; bounds.x_min = Twips::min(bounds.x_min, x); bounds.x_max = Twips::max(bounds.x_max, x); bounds.y_min = Twips::min(bounds.y_min, y); bounds.y_max = Twips::max(bounds.y_max, y); } swf::ShapeRecord::CurvedEdge { control_delta_x, control_delta_y, anchor_delta_x, anchor_delta_y, } => { x += *control_delta_x; y += *control_delta_y; bounds.x_min = Twips::min(bounds.x_min, x); bounds.x_max = Twips::max(bounds.x_max, x); bounds.y_min = Twips::min(bounds.y_min, y); bounds.y_max = Twips::max(bounds.y_max, y); x += *anchor_delta_x; y += *anchor_delta_y; bounds.x_min = Twips::min(bounds.x_min, x); bounds.x_max = Twips::max(bounds.x_max, x); bounds.y_min = Twips::min(bounds.y_min, y); bounds.y_max = Twips::max(bounds.y_max, y); } } } if bounds.x_max < bounds.x_min || bounds.y_max < bounds.y_min { bounds = Default::default(); } bounds } /// `DrawPath` represents a solid fill or a stroke. /// Fills are always closed paths, while strokes may be open or closed. /// Closed paths will have the first point equal to the last point. #[derive(Debug, PartialEq, Clone)] pub enum DrawPath<'a> { Stroke { style: &'a LineStyle, is_closed: bool, commands: Vec, }, Fill { style: &'a FillStyle, commands: Vec, }, } /// `DistilledShape` represents a ready-to-be-consumed collection of paths (both fills and strokes) /// that has been converted down from another source (such as SWF's `swf::Shape` format). #[derive(Debug, PartialEq, Clone)] pub struct DistilledShape<'a> { pub paths: Vec>, pub shape_bounds: BoundingBox, pub edge_bounds: BoundingBox, pub id: CharacterId, } impl<'a> From<&'a swf::Shape> for DistilledShape<'a> { fn from(shape: &'a Shape) -> Self { Self { paths: ShapeConverter::from_shape(shape).into_commands(), shape_bounds: (&shape.shape_bounds).into(), edge_bounds: (&shape.edge_bounds).into(), id: shape.id, } } } /// `DrawCommands` trace the outline of a path. /// Fills follow the even-odd fill rule, with opposite winding for holes. #[derive(Debug, PartialEq, Clone)] pub enum DrawCommand { MoveTo { x: Twips, y: Twips, }, LineTo { x: Twips, y: Twips, }, CurveTo { x1: Twips, y1: Twips, x2: Twips, y2: Twips, }, } impl DrawCommand { pub fn end_point(&self) -> (Twips, Twips) { match self { DrawCommand::MoveTo { x, y } => (*x, *y), DrawCommand::LineTo { x, y } => (*x, *y), DrawCommand::CurveTo { x2, y2, .. } => (*x2, *y2), } } } #[derive(Debug, Copy, Clone)] struct Point { x: Twips, y: Twips, is_bezier_control: bool, } /// A path segment is a series of edges linked togerther. /// Fill paths are directed, because the winding determines the fill-rule. /// Stroke paths are undirected. #[derive(Debug)] struct PathSegment { pub points: Vec, } impl PathSegment { fn new(start: (Twips, Twips)) -> Self { Self { points: vec![Point { x: start.0, y: start.1, is_bezier_control: false, }], } } /// Flips the direction of the path segment. /// Flash fill paths are dual-sided, with fill style 1 indicating the positive side /// and fill style 0 indicating the negative. We have to flip fill style 0 paths /// in order to link them to fill style 1 paths. fn flip(&mut self) { self.points.reverse(); } /// Adds an edge to the end of the path segment. fn add_point(&mut self, point: Point) { self.points.push(point); } fn is_empty(&self) -> bool { self.points.len() <= 1 } fn start(&self) -> (Twips, Twips) { let pt = &self.points.first().unwrap(); (pt.x, pt.y) } fn end(&self) -> (Twips, Twips) { let pt = &self.points.last().unwrap(); (pt.x, pt.y) } fn is_closed(&self) -> bool { self.start() == self.end() } /// Attempts to merge another path segment. /// One path's start must meet the other path's end. /// Returns true if the merge is successful. fn try_merge(&mut self, other: &mut PathSegment, directed: bool) -> bool { // Note that the merge point will be duplicated, so we want to slice it off one end. [1..] if other.end() == self.start() { std::mem::swap(&mut self.points, &mut other.points); self.points.extend_from_slice(&other.points[1..]); true } else if self.end() == other.start() { self.points.extend_from_slice(&other.points[1..]); true } else if !directed && self.end() == other.end() { other.flip(); self.points.extend_from_slice(&other.points[1..]); true } else if !directed && self.start() == other.start() { other.flip(); std::mem::swap(&mut self.points, &mut other.points); self.points.extend_from_slice(&other.points[1..]); true } else { false } } fn into_draw_commands(self) -> impl Iterator { assert!(self.points.len() > 1); let mut i = self.points.into_iter(); let first = i.next().unwrap(); std::iter::once(DrawCommand::MoveTo { x: first.x, y: first.y, }) .chain(std::iter::from_fn(move || match i.next() { Some(Point { is_bezier_control: false, x, y, }) => Some(DrawCommand::LineTo { x, y }), Some(Point { is_bezier_control: true, x, y, }) => { let end = i.next().expect("Bezier without endpoint"); Some(DrawCommand::CurveTo { x1: x, y1: y, x2: end.x, y2: end.y, }) } None => None, })) } } /// The internal path structure used by ShapeConverter. /// /// Each path is uniquely identified by its fill/stroke style. But Flash gives /// the path edges as an "edge soup" -- they can arrive in an arbitrary order. /// We have to link the edges together for each path. This structure contains /// a list of path segment, and each time a path segment is added, it will try /// to merge it with an existing segment. #[derive(Debug)] struct PendingPath { /// The list of path segments for this fill/stroke. /// For fills, this should turn into a list of closed paths when the shape is complete. /// Strokes may or may not be closed. segments: Vec, } impl PendingPath { fn new() -> Self { Self { segments: vec![] } } fn merge_path(&mut self, mut new_segment: PathSegment, directed: bool) { if !new_segment.is_empty() { if let Some(i) = self .segments .iter_mut() .position(|segment| segment.try_merge(&mut new_segment, directed)) { new_segment = self.segments.swap_remove(i); self.merge_path(new_segment, directed); } else { // Couldn't merge the segment any further to an existing segment. Add it to list. self.segments.push(new_segment); } } } fn into_draw_commands(self) -> impl Iterator { self.segments .into_iter() .map(PathSegment::into_draw_commands) .flatten() } } /// `PendingPathMap` maps from style IDs to the path associated with that style. /// Each path is uniquely identified by its style ID (until the style list changes). /// Style IDs tend to be sequential, so we just use a `Vec`. #[derive(Debug)] pub struct PendingPathMap(FnvHashMap); impl PendingPathMap { fn new() -> Self { Self(FnvHashMap::default()) } fn merge_path(&mut self, path: ActivePath, directed: bool) { let pending_path = self.0.entry(path.style_id).or_insert_with(PendingPath::new); pending_path.merge_path(path.segment, directed); } } #[derive(Debug)] pub struct ActivePath { style_id: NonZeroU32, segment: PathSegment, } impl ActivePath { fn new(style_id: NonZeroU32, start: (Twips, Twips)) -> Self { Self { style_id, segment: PathSegment::new(start), } } fn add_point(&mut self, point: Point) { self.segment.add_point(point) } fn flip(&mut self) { self.segment.flip() } } pub struct ShapeConverter<'a> { // SWF shape commands. iter: std::slice::Iter<'a, swf::ShapeRecord>, // Pen position. x: Twips, y: Twips, // Fill styles and line styles. // These change from StyleChangeRecords, and a flush occurs when these change. fill_styles: &'a [swf::FillStyle], line_styles: &'a [swf::LineStyle], fill_style0: Option, fill_style1: Option, line_style: Option, // Paths. These get flushed when the shape is complete // and for each new layer. fills: PendingPathMap, strokes: PendingPathMap, // Output. commands: Vec>, } impl<'a> ShapeConverter<'a> { const DEFAULT_CAPACITY: usize = 512; fn from_shape(shape: &'a swf::Shape) -> Self { ShapeConverter { iter: shape.shape.iter(), x: Twips::new(0), y: Twips::new(0), fill_styles: &shape.styles.fill_styles, line_styles: &shape.styles.line_styles, fill_style0: None, fill_style1: None, line_style: None, fills: PendingPathMap::new(), strokes: PendingPathMap::new(), commands: Vec::with_capacity(Self::DEFAULT_CAPACITY), } } fn into_commands(mut self) -> Vec> { while let Some(record) = self.iter.next() { match record { ShapeRecord::StyleChange(style_change) => { if let Some((x, y)) = style_change.move_to { self.x = x; self.y = y; // We've lifted the pen, so we're starting a new path. // Flush the previous path. self.flush_paths(); } if let Some(ref styles) = style_change.new_styles { // A new style list is also used to indicate a new drawing layer. self.flush_layer(); self.fill_styles = &styles.fill_styles[..]; self.line_styles = &styles.line_styles[..]; } if let Some(fs) = style_change.fill_style_1 { if let Some(path) = self.fill_style1.take() { self.fills.merge_path(path, true); } self.fill_style1 = if fs != 0 { let id = NonZeroU32::new(fs).unwrap(); Some(ActivePath::new(id, (self.x, self.y))) } else { None } } if let Some(fs) = style_change.fill_style_0 { if let Some(mut path) = self.fill_style0.take() { if !path.segment.is_empty() { path.flip(); self.fills.merge_path(path, true); } } self.fill_style0 = if fs != 0 { let id = NonZeroU32::new(fs).unwrap(); Some(ActivePath::new(id, (self.x, self.y))) } else { None } } if let Some(ls) = style_change.line_style { if let Some(path) = self.line_style.take() { self.strokes.merge_path(path, false); } self.line_style = if ls != 0 { let id = NonZeroU32::new(ls).unwrap(); Some(ActivePath::new(id, (self.x, self.y))) } else { None } } } ShapeRecord::StraightEdge { delta_x, delta_y } => { self.x += *delta_x; self.y += *delta_y; self.visit_point(Point { x: self.x, y: self.y, is_bezier_control: false, }); } ShapeRecord::CurvedEdge { control_delta_x, control_delta_y, anchor_delta_x, anchor_delta_y, } => { let x1 = self.x + *control_delta_x; let y1 = self.y + *control_delta_y; self.visit_point(Point { x: x1, y: y1, is_bezier_control: true, }); let x2 = x1 + *anchor_delta_x; let y2 = y1 + *anchor_delta_y; self.visit_point(Point { x: x2, y: y2, is_bezier_control: false, }); self.x = x2; self.y = y2; } } } // Flush any open paths. self.flush_layer(); self.commands } /// Adds a point to the current path for the active fills/strokes. fn visit_point(&mut self, point: Point) { if let Some(path) = &mut self.fill_style0 { path.add_point(point) } if let Some(path) = &mut self.fill_style1 { path.add_point(point) } if let Some(path) = &mut self.line_style { path.add_point(point) } } /// When the pen jumps to a new position, we reset the active path. fn flush_paths(&mut self) { // Move the current paths to the active list. if let Some(path) = self.fill_style1.take() { self.fill_style1 = Some(ActivePath::new(path.style_id, (self.x, self.y))); self.fills.merge_path(path, true); } if let Some(mut path) = self.fill_style0.take() { self.fill_style0 = Some(ActivePath::new(path.style_id, (self.x, self.y))); if !path.segment.is_empty() { path.flip(); self.fills.merge_path(path, true); } } if let Some(path) = self.line_style.take() { self.line_style = Some(ActivePath::new(path.style_id, (self.x, self.y))); self.strokes.merge_path(path, false); } } /// When a new layer starts, all paths are flushed and turned into drawing commands. fn flush_layer(&mut self) { self.flush_paths(); self.fill_style0 = None; self.fill_style1 = None; self.line_style = None; //let fills = std::mem::replace(&mut self.fills.0, FnvHashMap::default()); //let strokes = std::mem::replace(&mut self.strokes.0, FnvHashMap::default()); // Draw fills, and then strokes. for (style_id, path) in self.fills.0.drain() { assert!(style_id.get() > 0); let style = &self.fill_styles[style_id.get() as usize - 1]; self.commands.push(DrawPath::Fill { style, commands: path.into_draw_commands().collect(), }); } // Strokes are drawn last because they always appear on top of fills in the same layer. // Because path segments can either be open or closed, we convert each stroke segment into // a separate draw command. // TODO(Herschel): Open strokes could be grouped together into a single path. for (style_id, path) in self.strokes.0.drain() { assert!(style_id.get() > 0); let style = &self.line_styles[style_id.get() as usize - 1]; for segment in path.segments { self.commands.push(DrawPath::Stroke { style, is_closed: segment.is_closed(), commands: segment.into_draw_commands().collect(), }); } } } } #[cfg(test)] mod tests { use super::*; const FILL_STYLES: [FillStyle; 1] = [FillStyle::Color(swf::Color { r: 255, g: 0, b: 0, a: 255, })]; const LINE_STYLES: [LineStyle; 0] = []; /// Convenience method to quickly make a shape, fn build_shape(records: Vec) -> swf::Shape { let bounds = calculate_shape_bounds(&records[..]); swf::Shape { version: 2, id: 1, shape_bounds: bounds.clone(), edge_bounds: bounds, has_fill_winding_rule: false, has_non_scaling_strokes: false, has_scaling_strokes: true, styles: swf::ShapeStyles { fill_styles: FILL_STYLES.to_vec(), line_styles: LINE_STYLES.to_vec(), }, shape: records, } } /// A simple solid square. #[test] fn basic_shape() { let shape = build_shape(vec![ ShapeRecord::StyleChange(swf::StyleChangeData { move_to: Some((Twips::from_pixels(100.0), Twips::from_pixels(100.0))), fill_style_0: None, fill_style_1: Some(1), line_style: None, new_styles: None, }), ShapeRecord::StraightEdge { delta_x: Twips::from_pixels(100.0), delta_y: Twips::from_pixels(0.0), }, ShapeRecord::StraightEdge { delta_x: Twips::from_pixels(0.0), delta_y: Twips::from_pixels(100.0), }, ShapeRecord::StraightEdge { delta_x: Twips::from_pixels(-100.0), delta_y: Twips::from_pixels(0.0), }, ShapeRecord::StraightEdge { delta_x: Twips::from_pixels(0.0), delta_y: Twips::from_pixels(-100.0), }, ]); let commands = ShapeConverter::from_shape(&shape).into_commands(); let expected = vec![DrawPath::Fill { style: &FILL_STYLES[0], commands: vec![ DrawCommand::MoveTo { x: Twips::from_pixels(100.0), y: Twips::from_pixels(100.0), }, DrawCommand::LineTo { x: Twips::from_pixels(200.0), y: Twips::from_pixels(100.0), }, DrawCommand::LineTo { x: Twips::from_pixels(200.0), y: Twips::from_pixels(200.0), }, DrawCommand::LineTo { x: Twips::from_pixels(100.0), y: Twips::from_pixels(200.0), }, DrawCommand::LineTo { x: Twips::from_pixels(100.0), y: Twips::from_pixels(100.0), }, ], }]; assert_eq!(commands, expected); } /// A solid square with one edge flipped (fillstyle0 instead of fillstyle1). #[test] fn flipped_edges() { let shape = build_shape(vec![ ShapeRecord::StyleChange(swf::StyleChangeData { move_to: Some((Twips::from_pixels(100.0), Twips::from_pixels(100.0))), fill_style_0: None, fill_style_1: Some(1), line_style: None, new_styles: None, }), ShapeRecord::StraightEdge { delta_x: Twips::from_pixels(100.0), delta_y: Twips::from_pixels(0.0), }, ShapeRecord::StraightEdge { delta_x: Twips::from_pixels(0.0), delta_y: Twips::from_pixels(100.0), }, ShapeRecord::StraightEdge { delta_x: Twips::from_pixels(-100.0), delta_y: Twips::from_pixels(0.0), }, ShapeRecord::StyleChange(swf::StyleChangeData { move_to: Some((Twips::from_pixels(100.0), Twips::from_pixels(100.0))), fill_style_0: Some(1), fill_style_1: Some(0), line_style: None, new_styles: None, }), ShapeRecord::StraightEdge { delta_x: Twips::from_pixels(0.0), delta_y: Twips::from_pixels(100.0), }, ]); let commands = ShapeConverter::from_shape(&shape).into_commands(); let expected = vec![DrawPath::Fill { style: &FILL_STYLES[0], commands: vec![ DrawCommand::MoveTo { x: Twips::from_pixels(100.0), y: Twips::from_pixels(200.0), }, DrawCommand::LineTo { x: Twips::from_pixels(100.0), y: Twips::from_pixels(100.0), }, DrawCommand::LineTo { x: Twips::from_pixels(200.0), y: Twips::from_pixels(100.0), }, DrawCommand::LineTo { x: Twips::from_pixels(200.0), y: Twips::from_pixels(200.0), }, DrawCommand::LineTo { x: Twips::from_pixels(100.0), y: Twips::from_pixels(200.0), }, ], }]; assert_eq!(commands, expected); } } /* SHAPEFLAG HITTEST (point-in-contour) * * To determine whether a point is inside a shape, we shoot a ray on the +x axis and calculate a winding number based * on the edges that intersect with the ray. * * For each edge: * if the edge cross the ray downward (+y), we add 1 to the winding number. * if the edge cross the ray upward (-y), we add -1 to the winding number. * * We must also handle intersection with edge endpoints consistently to avoid double counting: * the initial point of an edge is considered for upwards rays. * the final point of an edge is considered for downward rays. * * For SWF shapes, edges with fillstyle1 use clockwise winding, and edges with fillstyle0 use CCW winding (flip them). * We ignore any edges with fills on both sides (interior edges). * * If the final winding number is odd, then the point is inside the shape (for default even-odd winding). * * For strokes, we calculate the distance to the line segment or curve and compare it to the stroke width. * Note that Flash renders with a minimum stroke width of 1px (20 twips) that we must account for. * TODO: We currently don't consider non-round endcaps or joins, or stroke scaling flags. */ /// Test whether the given point in object space is contained within the contour of the given shape. /// local_matrix is used to calculate the proper stroke widths. pub fn shape_hit_test( shape: &swf::Shape, (point_x, point_y): (Twips, Twips), local_matrix: &Matrix, ) -> bool { // Transform point to local space. let mut x = Twips::new(0); let mut y = Twips::new(0); let mut winding = 0; let mut has_fill_style0: bool = false; let mut has_fill_style1: bool = false; let min_width = f64::from(stroke_minimum_width(local_matrix)); let mut stroke_width = None; let mut line_styles = &shape.styles.line_styles; for record in &shape.shape { match record { swf::ShapeRecord::StyleChange(style_change) => { // New styles indicates a new layer; // Check if the point is within the current layer, then reset winding. if let Some(new_styles) = &style_change.new_styles { if winding & 0b1 != 0 { return true; } line_styles = &new_styles.line_styles; winding = 0; } if let Some((move_x, move_y)) = style_change.move_to { x = move_x; y = move_y; } if let Some(i) = style_change.fill_style_0 { has_fill_style0 = i > 0; } if let Some(i) = style_change.fill_style_1 { has_fill_style1 = i > 0; } if let Some(i) = style_change.line_style { stroke_width = if i > 0 { // Flash renders strokes with a 1px minimum width. if let Some(line_style) = line_styles.get(i as usize - 1) { let width = line_style.width.get() as f64; let scaled_width = 0.5 * width.max(min_width); Some((scaled_width, scaled_width * scaled_width)) } else { None } } else { None }; } } swf::ShapeRecord::StraightEdge { delta_x, delta_y } => { let x1 = x + *delta_x; let y1 = y + *delta_y; // If this edge has a fill style on only one-side, check for a crossing. if has_fill_style1 { if !has_fill_style0 { winding += winding_number_line((point_x, point_y), (x, y), (x1, y1)); } } else if has_fill_style0 { winding += winding_number_line((point_x, point_y), (x1, y1), (x, y)); } if let Some(width) = stroke_width { if hit_test_stroke((point_x, point_y), (x, y), (x1, y1), width) { return true; } } x = x1; y = y1; } swf::ShapeRecord::CurvedEdge { control_delta_x, control_delta_y, anchor_delta_x, anchor_delta_y, } => { let x1 = x + *control_delta_x; let y1 = y + *control_delta_y; let x2 = x1 + *anchor_delta_x; let y2 = y1 + *anchor_delta_y; // If this edge has a fill style on only one-side, check for a crossing. if has_fill_style1 { if !has_fill_style0 { winding += winding_number_curve((point_x, point_y), (x, y), (x1, y1), (x2, y2)); } } else if has_fill_style0 { winding += winding_number_curve((point_x, point_y), (x2, y2), (x1, y1), (x, y)); } if let Some(width) = stroke_width { if hit_test_stroke_curve((point_x, point_y), (x, y), (x1, y1), (x2, y2), width) { return true; } } x = x2; y = y2; } } } winding & 0b1 != 0 } /// Test whether the given point is contained with in the paths specified by the draw commands. pub fn draw_command_fill_hit_test( commands: &[DrawCommand], (point_x, point_y): (Twips, Twips), ) -> bool { let mut x = Twips::new(0); let mut y = Twips::new(0); let mut winding = 0; // Draw command only contains a single fill, so don't have to worry about fill styles. for command in commands { match *command { DrawCommand::MoveTo { x: x1, y: y1 } => { x = x1; y = y1; } DrawCommand::LineTo { x: x1, y: y1 } => { winding += winding_number_line((point_x, point_y), (x, y), (x1, y1)); x = x1; y = y1; } DrawCommand::CurveTo { x1, y1, x2, y2 } => { winding += winding_number_curve((point_x, point_y), (x, y), (x1, y1), (x2, y2)); x = x2; y = y2; } } } winding & 0b1 != 0 } /// Test whether the given point is contained with in the strokes specified by the draw commands. /// local_matrix is used to calculate the minimum stroke width. pub fn draw_command_stroke_hit_test( commands: &[DrawCommand], stroke_width: Twips, (point_x, point_y): (Twips, Twips), local_matrix: &Matrix, ) -> bool { let stroke_min_width = f64::from(stroke_minimum_width(local_matrix)); let stroke_width = 0.5 * f64::max(stroke_width.get().into(), stroke_min_width); let stroke_widths = (stroke_width, stroke_width * stroke_width); let mut x = Twips::default(); let mut y = Twips::default(); for command in commands { match *command { DrawCommand::MoveTo { x: x1, y: y1 } => { x = x1; y = y1; } DrawCommand::LineTo { x: x1, y: y1 } => { if hit_test_stroke((point_x, point_y), (x, y), (x1, y1), stroke_widths) { return true; } x = x1; y = y1; } DrawCommand::CurveTo { x1, y1, x2, y2 } => { if hit_test_stroke_curve( (point_x, point_y), (x, y), (x1, y1), (x2, y2), stroke_widths, ) { return true; } x = x2; y = y2; } } } false } /// Given a matrix, calculates the scale for stroke widths. /// TODO: Verify the actual behavior; I think it's more like the average between scaleX and scaleY. /// Does not yet support vertical/horizontal stroke scaling flags. /// This might be better to add as a method to Matrix. fn stroke_minimum_width(matrix: &Matrix) -> f32 { let sx = (matrix.a * matrix.a + matrix.b * matrix.b).sqrt(); let sy = (matrix.c * matrix.c + matrix.d * matrix.d).sqrt(); let scale = sx.max(sy); 20.0 * scale } /// Returns whether the given point is inside the stroked line segment. /// `width_sq` should be the squared width of the stroke. fn hit_test_stroke( (point_x, point_y): (Twips, Twips), (x0, y0): (Twips, Twips), (x1, y1): (Twips, Twips), (stroke_width, stroke_width_sq): (f64, f64), ) -> bool { let px = point_x.get() as f64; let py = point_y.get() as f64; let x0 = x0.get() as f64; let y0 = y0.get() as f64; let x1 = x1.get() as f64; let y1 = y1.get() as f64; // Early exit: out of bounds let x_min = x0.min(x1); let x_max = x0.max(x1); if px < x_min - stroke_width || px > x_max + stroke_width { return false; } let y_min = y0.min(y1); let y_max = y0.max(y1); if py < y_min - stroke_width || py > y_max + stroke_width { return false; } // AB is the segment from (x0, y0) to (x1, y1) and P is (point_x, point_y). // P // . // . // A----->B // If AP dot AB is <= 0.0, then PA is pointing away from AB, so A is the closest point. let abx = x1 - x0; let aby = y1 - y0; let apx = px - x0; let apy = py - y0; let dot_a = abx * apx + aby * apy; let dist = if dot_a <= 0.0 { apx * apx + apy * apy } else { // If BP dot AB is >= 0.0, then BP is pointing away from BA, so B is the closest point. let bpx = px - x1; let bpy = py - y1; let dot_b = abx * bpx + aby * bpy; if dot_b >= 0.0 { bpx * bpx + bpy * bpy } else { // Otherwise, the closest point will be within the interval of the segment. // Project the point onto the segment. let len = abx * abx + aby * aby; let ex = apx - dot_a * abx / len; let ey = apy - dot_a * aby / len; ex * ex + ey * ey } }; dist <= stroke_width_sq } /// Returns whether the given point is inside the stroked bezier curve. /// `width_sq` should be the squared width of the stroke. fn hit_test_stroke_curve( (point_x, point_y): (Twips, Twips), (x0, y0): (Twips, Twips), (x1, y1): (Twips, Twips), (x2, y2): (Twips, Twips), (stroke_width, stroke_width_sq): (f64, f64), ) -> bool { let px = point_x.get() as f64; let py = point_y.get() as f64; let x0 = x0.get() as f64; let y0 = y0.get() as f64; let x1 = x1.get() as f64; let y1 = y1.get() as f64; let x2 = x2.get() as f64; let y2 = y2.get() as f64; // Early exit: out of bounds // TODO: Since this involves an expensive cubic, probably wortwhile to calculate the tight bounds for the curve: // https://www.iquilezles.org/www/articles/bezierbbox/bezierbbox.htm let x_min = x0.min(x1).min(x2); let x_max = x0.max(x1).max(x2); if px < x_min - stroke_width || px > x_max + stroke_width { return false; } let y_min = y0.min(y1).min(y2); let y_max = y0.max(y1).max(y2); if py < y_min - stroke_width || py > y_max + stroke_width { return false; } // The closest point on the curve will be normal to the curve. // The tangent of a quadratic bezier: // C'(t) = -2 * (1-t) * P0 + 2 * (1-t) * P1 + 2*t*P2 // Dot product to determine when we are perpendicular to the tangent. // (point - C(t)) . C'(t) = 0 // The result is a cubic polynomial that we can solve for. // After solving this polynomial, we choose the t with [0, 1.0] that gives us the minimum distance // (also considering the endcaps). // via http://blog.gludion.com/2009/08/distance-to-quadratic-bezier-curve.html let ax = x1 - x0; let ay = y1 - y0; let bx = x2 - x1 - ax; let by = y2 - y1 - ay; let mx = x0 - px; let my = y0 - py; let a = bx * bx + by * by; let b = 3.0 * (ax * bx + ay * by); let c = 2.0 * (ax * ax + ay * ay) + (mx * bx + my * by); let d = mx * ax + my * ay; let distance_to_curve = |t| -> f64 { // Sample bezier at the given t and return distance to the point. let comp_t = 1.0 - t; let cx = comp_t * comp_t * x0 + 2.0 * comp_t * t * x1 + t * t * x2; let cy = comp_t * comp_t * y0 + 2.0 * comp_t * t * y1 + t * t * y2; let dx = cx - px; let dy = cy - py; dx * dx + dy * dy }; // Test end-caps let mut dist = distance_to_curve(0.0); dist = dist.min(distance_to_curve(1.0)); // Test roots. for t in solve_cubic(a, b, c, d) { if t >= 0.0 && t <= 1.0 { dist = dist.min(distance_to_curve(t)); } } dist <= stroke_width_sq } /// Calculates the winding number for a line segment relative to the given point. fn winding_number_line( (point_x, point_y): (Twips, Twips), (x0, y0): (Twips, Twips), (x1, y1): (Twips, Twips), ) -> i32 { let point_x = point_x.get() as f64; let point_y = point_y.get() as f64; let x0 = x0.get() as f64; let y0 = y0.get() as f64; let x1 = x1.get() as f64; let y1 = y1.get() as f64; // Adjust winding number if we are on the left side of the segment. // An upward segment (-y) increments the winding number (including the initial endpoint). // A downward segment (+y) decrements the winding number (including the final endpoint) // Perp-dot indicates which side of the segment the point is on. if y0 <= point_y { if y1 > point_y { let val = (x1 - x0) * (point_y - y0) - (y1 - y0) * (point_x - x0); if val > 0.0 { return 1; } } } else if y1 <= point_y { let val = (x1 - x0) * (point_y - y0) - (y1 - y0) * (point_x - x0); if val < 0.0 { return -1; } } 0 } /// Calculates the winding number for a bezier curve around the given point. fn winding_number_curve( (point_x, point_y): (Twips, Twips), (ax0, ay0): (Twips, Twips), (ax1, ay1): (Twips, Twips), (ax2, ay2): (Twips, Twips), ) -> i32 { // Intersect a ray on the +x axis with the quadratic bezier. // // Translate so the test point and ray is at the origin. // The ray-curve intersection is solving the quadratic: // y_0*(1-t)^2 + y_1*2*t*(1-t) + y_2*t^2 = 0 // However, there are two issues: // 1) Solving the quadratic needs to be numerically robust, particularly near the endpoints 0.0 and 1.0, and as the curve is tangent to the ray. // We use the "Citardauq" method for improved numerical stability. // 2) The convention for including/excluding endpoints needs to act similarly to lines, with the initial point included if the curve is "downward", // and the final point included if the curve is pointing "upward". This is complicated by the fact that the curve could be tangent to the ray // at the endpoint (this is still considered "upward" or "downward" depending on the slope at earlier t). // We solve this by splitting the curve into y-monotonic subcurves. This is helpful because // a) each subcurve will have 1 intersection with the ray // b) if the subcurve surrounds the ray, we know it has an intersection without having to check if t is in [0, 1] // c) we can determine the winding of the segment upward/downward by comparing the subcurve endpoints, also properly handling the endpoint convention. let x0 = ax0.get() - point_x.get(); let y0 = ay0.get() - point_y.get(); let x1 = ax1.get() - point_x.get(); let y1 = ay1.get() - point_y.get(); let x2 = ax2.get() - point_x.get(); let y2 = ay2.get() - point_y.get(); // Early exit: all control points out of bounds. if (y0 < 0 && y1 < 0 && y2 < 0) || (y0 > 0 && y1 > 0 && y2 > 0) || (x0 <= 0 && x1 <= 0 && x2 <= 0) { return 0; } let x0 = x0 as f64; let y0 = y0 as f64; let x1 = x1 as f64; let y1 = y1 as f64; let x2 = x2 as f64; let y2 = y2 as f64; let a = y0 - 2.0 * y1 + y2; let b = 2.0 * (y1 - y0); let c = y0; let roots = solve_quadratic(a, b, c); if roots.is_empty() { return 0; } // Split the curve into two y-monotonic segments. let mut y_start = y0; let mut y_end = if roots.len() == 1 { // Linear, so already monotonic. y2 } else { // Find the extrema point where the curve is horizontal. // This is the point that splits the curve into 2 y-monotonic segments. let t_extrema = -b / (2.0 * a); a * t_extrema * t_extrema + b * t_extrema + c }; let ax = x0 - 2.0 * x1 + x2; let bx = 2.0 * (x1 - x0); let mut winding = 0; for t in roots { // Verify that this monotonic segment straddles the ray, and choose winding direction. // This also handles the endpoint conventions. let direction = if y_end > y_start { // Downward edge: initial point included, increments winding. if y_start > 0.0 || y_end <= 0.0 { 0 } else { 1 } } else if y_start > y_end { // Upward edge: final point included, increments winding. if y_start <= 0.0 || y_end > 0.0 { 0 } else { -1 } } else { 0 }; // If curve point is to the right of the ray origin, the ray will hit it. // We don't have to do the problematic 0 <= t <= 1 check because this vertical slice is guaranteed // to contain the monotonic segment, and our roots are returned in order by `solve_quadratic`. // Adjust the winding as appropriate. if direction != 0 { let t_x = x0 + bx * t + ax * t * t; if t_x > 0.0 { winding += direction; } } // Advance to next monotonic segment y_start = y_end; y_end = y2; } winding } const COEFFICIENT_EPSILON: f64 = 0.0000001; /// Returns the roots of the quadratic ax^2 + bx + c = 0. /// The roots may not be unique. /// Uses the "Citardauq" formula for numerical stability. /// Originally from https://github.com/linebender/kurbo/blob/master/src/common.rs /// See https://math.stackexchange.com/questions/866331 fn solve_quadratic(a: f64, b: f64, c: f64) -> SmallVec<[f64; 2]> { let mut result = SmallVec::new(); let sc0 = c * a.recip(); let sc1 = b * a.recip(); if !sc0.is_finite() || !sc1.is_finite() { // c2 is zero or very small, treat as linear eqn let root = -c / b; if root.is_finite() { result.push(root); } return result; } let arg = sc1 * sc1 - 4.0 * sc0; let root1 = if !arg.is_finite() { // Likely, calculation of sc1 * sc1 overflowed. Find one root // using sc1 x + x² = 0, other root as sc0 / root1. -sc1 } else { if arg < 0.0 { return result; } -0.5 * (sc1 + arg.sqrt().copysign(sc1)) }; let root2 = sc0 / root1; // Sort just to be friendly and make results deterministic. if root2 > root1 { result.push(root1); result.push(root2); } else { result.push(root2); result.push(root1); } result } /// Returns the roots of a cubic polynomial, ax^3 + bx^2 + cx + d = 0 /// from http://www.cplusplus.com/forum/beginner/234717/ /// The roots are not necessarily unique. /// TODO: This probably isn't numerically robust #[allow(clippy::many_single_char_names)] fn solve_cubic(a: f64, b: f64, c: f64, d: f64) -> SmallVec<[f64; 3]> { let mut roots = SmallVec::new(); if a.abs() <= COEFFICIENT_EPSILON { // Fall back to quadratic formula. roots.extend_from_slice(&solve_quadratic(b, c, d)); return roots; } // Reduce to a "depressed cubic", x^3 + px + q = 0 // https://en.wikipedia.org/wiki/Cubic_equation#Cardano's_formula let p = (b * b - 3.0 * a * c) / (9.0 * a * a); let q = (9.0 * a * b * c - 27.0 * a * a * d - 2.0 * b * b * b) / (54.0 * a * a * a); let offset = b / (3.0 * a); let disc = p * p * p - q * q; // The discriminant determines the number of real roots. if disc > 0.0 { let theta = f64::acos(q / (p * f64::sqrt(p))); let r = 2.0 * f64::sqrt(p); let t0 = r * f64::cos(theta / 3.0) - offset; let t1 = r * f64::cos((theta + 2.0 * std::f64::consts::PI) / 3.0) - offset; let t2 = r * f64::cos((theta + 4.0 * std::f64::consts::PI) / 3.0) - offset; roots.push(t0); roots.push(t1); roots.push(t2); } else { let gamma1 = f64::cbrt(q + f64::sqrt(-disc)); let gamma2 = f64::cbrt(q - f64::sqrt(-disc)); let t0 = gamma1 + gamma2 - offset; let t1 = -0.5 * (gamma1 + gamma2) - offset; if disc == 0.0 { roots.push(t0); roots.push(t1); } else { roots.push(t0); } } roots } /// Converts an SWF glyph into an SWF shape, for ease of use by rendering backends. pub fn swf_glyph_to_shape(glyph: &swf::Glyph) -> swf::Shape { // Per SWF19 p.164, the FontBoundsTable can contain empty bounds for every glyph (reserved). // SWF19 says this is true through SWFv7, but it seems like it might be generally true? // In any case, we have to be sure to calculate the shape bounds ourselves to make a proper // SVG. let bounds = glyph .bounds .clone() .filter(|b| b.x_min != b.x_max || b.y_min != b.y_max) .unwrap_or_else(|| calculate_shape_bounds(&glyph.shape_records[..])); swf::Shape { version: 2, id: 0, shape_bounds: bounds.clone(), edge_bounds: bounds, has_fill_winding_rule: false, has_non_scaling_strokes: false, has_scaling_strokes: true, styles: swf::ShapeStyles { fill_styles: vec![swf::FillStyle::Color(swf::Color { r: 255, g: 255, b: 255, a: 255, })], line_styles: vec![], }, shape: glyph.shape_records.clone(), } }