Implement some 3D transform code, untested as of yet

geometry/src/lib.rs

@@ -28,4 +28,5 @@ pub mod segments;
 pub mod simd;
 pub mod stroke;
 pub mod transform;
+pub mod transform3d;
 pub mod util;

geometry/src/monotonic.rs

@@ -10,7 +10,6 @@
 
 //! Converts paths to monotonically increasing/decreasing segments.
 
-use crate::outline::Contour;
 use crate::segment::{Segment, SegmentKind};
 use arrayvec::ArrayVec;
 

geometry/src/point.rs

@@ -14,6 +14,8 @@ use crate::simd::F32x4;
 use euclid::Point2D;
 use std::ops::{Add, Mul, Sub};
 
+// 2D points.
+
 #[derive(Clone, Copy, Debug, Default)]
 pub struct Point2DF32(pub F32x4);
 
@@ -38,6 +40,12 @@ impl Point2DF32 {
         Point2D::new(self.0[0], self.0[1])
     }
 
+    // TODO(pcwalton): Optimize this!
+    #[inline]
+    pub fn to_4d(self) -> Point4DF32 {
+        Point4DF32::new(self.0[0], self.0[1], 0.0, 1.0)
+    }
+
     #[inline]
     pub fn x(&self) -> f32 {
         self.0[0]
@@ -90,3 +98,58 @@ impl Mul<Point2DF32> for Point2DF32 {
         Point2DF32(self.0 * other.0)
     }
 }
+
+// 3D homogeneous points.
+
+#[derive(Clone, Copy, Debug, Default)]
+pub struct Point4DF32(pub F32x4);
+
+impl Point4DF32 {
+    #[inline]
+    pub fn new(x: f32, y: f32, z: f32, w: f32) -> Point4DF32 {
+        Point4DF32(F32x4::new(x, y, z, w))
+    }
+
+    #[inline]
+    pub fn splat(value: f32) -> Point4DF32 {
+        Point4DF32(F32x4::splat(value))
+    }
+
+    #[inline]
+    pub fn to_2d(self) -> Point2DF32 {
+        Point2DF32(self.0)
+    }
+
+    #[inline]
+    pub fn x(self) -> f32 {
+        self.0[0]
+    }
+
+    #[inline]
+    pub fn y(self) -> f32 {
+        self.0[1]
+    }
+
+    #[inline]
+    pub fn z(self) -> f32 {
+        self.0[2]
+    }
+
+    #[inline]
+    pub fn w(self) -> f32 {
+        self.0[3]
+    }
+
+    #[inline]
+    pub fn perspective_divide(self) -> Point4DF32 {
+        self * Point4DF32::splat(1.0 / self.w())
+    }
+}
+
+impl Mul<Point4DF32> for Point4DF32 {
+    type Output = Point4DF32;
+    #[inline]
+    fn mul(self, other: Point4DF32) -> Point4DF32 {
+        Point4DF32(self.0 * other.0)
+    }
+}

geometry/src/simd.rs

@@ -151,6 +151,11 @@ mod scalar {
             (F32x4([self[0], other[0], self[1], other[1]]),
              F32x4([self[2], other[2], self[3], other[3]]))
         }
+
+        #[inline]
+        pub fn transpose4(a: &mut F32x4, b: &mut F32x4, c: &mut F32x4, d: &mut F32x4) {
+            unimplemented!()
+        }
     }
 
     impl Index<usize> for F32x4 {
@@ -442,6 +447,13 @@ mod x86 {
                 )
             }
         }
+
+        #[inline]
+        pub fn transpose_4x4(a: &mut F32x4, b: &mut F32x4, c: &mut F32x4, d: &mut F32x4) {
+            unsafe {
+                x86_64::_MM_TRANSPOSE4_PS(&mut a.0, &mut b.0, &mut c.0, &mut d.0)
+            }
+        }
     }
 
     impl Default for F32x4 {

geometry/src/transform3d.rs

@@ -0,0 +1,146 @@
+// pathfinder/geometry/src/transform3d.rs
+//
+// Copyright © 2019 The Pathfinder Project Developers.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+//! 3D transforms that can be applied to paths.
+
+use crate::point::Point4DF32;
+use crate::simd::F32x4;
+
+/// An transform, optimized with SIMD.
+///
+/// In column-major order.
+#[derive(Clone, Copy)]
+pub struct Transform3DF32 {
+    c0: F32x4,
+    c1: F32x4,
+    c2: F32x4,
+    c3: F32x4,
+}
+
+impl Default for Transform3DF32 {
+    #[inline]
+    fn default() -> Transform3DF32 {
+        Transform3DF32 {
+            c0: F32x4::new(1.0, 0.0, 0.0, 0.0),
+            c1: F32x4::new(0.0, 1.0, 0.0, 0.0),
+            c2: F32x4::new(0.0, 0.0, 1.0, 0.0),
+            c3: F32x4::new(0.0, 0.0, 0.0, 1.0),
+        }
+    }
+}
+
+impl Transform3DF32 {
+    #[inline]
+    pub fn row_major(m00: f32, m01: f32, m02: f32, m03: f32,
+                     m10: f32, m11: f32, m12: f32, m13: f32,
+                     m20: f32, m21: f32, m22: f32, m23: f32,
+                     m30: f32, m31: f32, m32: f32, m33: f32)
+                     -> Transform3DF32 {
+        Transform3DF32 {
+            c0: F32x4::new(m00, m10, m20, m30),
+            c1: F32x4::new(m01, m11, m21, m31),
+            c2: F32x4::new(m02, m12, m22, m32),
+            c3: F32x4::new(m03, m13, m23, m33),
+        }
+    }
+
+    #[inline]
+    pub fn scale(x: f32, y: f32, z: f32) -> Transform3DF32 {
+        Transform3DF32::row_major(  x, 0.0, 0.0, 0.0,
+                                  0.0,   y, 0.0, 0.0,
+                                  0.0, 0.0,   z, 0.0,
+                                  0.0, 0.0, 0.0, 1.0)
+    }
+
+    #[inline]
+    pub fn translate(x: f32, y: f32, z: f32) -> Transform3DF32 {
+        Transform3DF32::row_major(1.0, 0.0, 0.0, x,
+                                  0.0, 1.0, 0.0, y,
+                                  0.0, 0.0, 1.0, z,
+                                  0.0, 0.0, 0.0, 1.0)
+    }
+
+    // TODO(pcwalton): Optimize.
+    pub fn rotate(roll: f32, pitch: f32, yaw: f32) -> Transform3DF32 {
+        let (cos_roll, sin_roll) = (roll.cos(), roll.sin());
+        let (cos_pitch, sin_pitch) = (pitch.cos(), pitch.sin());
+        let (cos_yaw, sin_yaw) = (yaw.cos(), yaw.sin());
+        let m00 = cos_yaw * cos_pitch;
+        let m01 = cos_yaw * sin_pitch * sin_roll - sin_yaw * cos_roll;
+        let m02 = cos_yaw * sin_pitch * sin_roll + sin_yaw * sin_roll;
+        let m10 = sin_yaw * cos_pitch;
+        let m11 = sin_yaw * sin_pitch * sin_roll + cos_yaw * cos_roll;
+        let m12 = sin_yaw * sin_pitch * cos_roll + cos_yaw * sin_roll;
+        let m20 = -sin_pitch;
+        let m21 = cos_pitch * sin_roll;
+        let m22 = cos_pitch * cos_roll;
+        Transform3DF32::row_major(m00, m01, m02, 0.0,
+                                  m10, m11, m12, 0.0,
+                                  m20, m21, m22, 0.0,
+                                  0.0, 0.0, 0.0, 1.0)
+    }
+
+    /// Just like `gluPerspective()`.
+    #[inline]
+    pub fn perspective(fov_y: f32, aspect: f32, z_near: f32, z_far: f32) -> Transform3DF32 {
+        let f = 1.0 / (fov_y * 0.5).tan();
+        let z_denom = 1.0 / (z_near - z_far);
+        let m00 = f / aspect;
+        let m11 = f;
+        let m22 = (z_far + z_near) * z_denom;
+        let m23 = 2.0 * z_far * z_near * z_denom;
+        let m32 = -1.0;
+        Transform3DF32::row_major(m00, 0.0, 0.0, 0.0,
+                                  0.0, m11, 0.0, 0.0,
+                                  0.0, 0.0, m22, m23,
+                                  0.0, 0.0, m32, 0.0)
+    }
+
+    #[inline]
+    pub fn transpose(&self) -> Transform3DF32 {
+        let mut m = *self;
+        F32x4::transpose_4x4(&mut m.c0, &mut m.c1, &mut m.c2, &mut m.c3);
+        m
+    }
+
+    // FIXME(pcwalton): Is this right, due to transposition? I think we may have to reverse the
+    // two.
+    //
+    // https://stackoverflow.com/a/18508113
+    #[inline]
+    pub fn post_mul(&self, other: &Transform3DF32) -> Transform3DF32 {
+        return Transform3DF32 {
+            c0: mul_row(self.c0, other),
+            c1: mul_row(self.c1, other),
+            c2: mul_row(self.c2, other),
+            c3: mul_row(self.c3, other),
+        };
+
+        fn mul_row(a_row: F32x4, b: &Transform3DF32) -> F32x4 {
+            let (a0, a1) = (F32x4::splat(a_row[0]), F32x4::splat(a_row[1]));
+            let (a2, a3) = (F32x4::splat(a_row[2]), F32x4::splat(a_row[3]));
+            a0 * b.c0 + a1 * b.c1 + a2 * b.c2 + a3 * b.c3
+        }
+    }
+
+    #[inline]
+    pub fn pre_mul(&self, other: &Transform3DF32) -> Transform3DF32 {
+        other.post_mul(self)
+    }
+
+    #[inline]
+    pub fn transform_point(&self, point: Point4DF32) -> Point4DF32 {
+        let term0 = self.c0 * F32x4::splat(point.x());
+        let term1 = self.c1 * F32x4::splat(point.y());
+        let term2 = self.c2 * F32x4::splat(point.z());
+        let term3 = self.c3 * F32x4::splat(point.w());
+        Point4DF32(term0 + term1 + term2 + term3)
+    }
+}