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use std::f64::consts::PI;
use std::ops::Mul;
/// The projection matrix which is used to project the 3D space to the 2D display panel
#[derive(Clone, Debug, Copy)]
pub struct ProjectionMatrix([[f64; 4]; 4]);
impl AsRef<[[f64; 4]; 4]> for ProjectionMatrix {
fn as_ref(&self) -> &[[f64; 4]; 4] {
&self.0
}
}
impl AsMut<[[f64; 4]; 4]> for ProjectionMatrix {
fn as_mut(&mut self) -> &mut [[f64; 4]; 4] {
&mut self.0
}
}
impl From<[[f64; 4]; 4]> for ProjectionMatrix {
fn from(data: [[f64; 4]; 4]) -> Self {
ProjectionMatrix(data)
}
}
impl Default for ProjectionMatrix {
fn default() -> Self {
ProjectionMatrix::rotate(PI, 0.0, 0.0)
}
}
impl Mul<ProjectionMatrix> for ProjectionMatrix {
type Output = ProjectionMatrix;
fn mul(self, other: ProjectionMatrix) -> ProjectionMatrix {
let mut ret = ProjectionMatrix::zero();
for r in 0..4 {
for c in 0..4 {
for k in 0..4 {
ret.0[r][c] += other.0[r][k] * self.0[k][c];
}
}
}
ret.normalize();
ret
}
}
impl Mul<(i32, i32, i32)> for ProjectionMatrix {
type Output = (i32, i32);
fn mul(self, (x, y, z): (i32, i32, i32)) -> (i32, i32) {
let (x, y, z) = (x as f64, y as f64, z as f64);
let m = self.0;
(
(x * m[0][0] + y * m[0][1] + z * m[0][2] + m[0][3]) as i32,
(x * m[1][0] + y * m[1][1] + z * m[1][2] + m[1][3]) as i32,
)
}
}
impl Mul<(f64, f64, f64)> for ProjectionMatrix {
type Output = (i32, i32);
fn mul(self, (x, y, z): (f64, f64, f64)) -> (i32, i32) {
let m = self.0;
(
(x * m[0][0] + y * m[0][1] + z * m[0][2] + m[0][3]) as i32,
(x * m[1][0] + y * m[1][1] + z * m[1][2] + m[1][3]) as i32,
)
}
}
impl ProjectionMatrix {
/// Returns the identity matrix
pub fn one() -> Self {
ProjectionMatrix([
[1.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 1.0],
])
}
/// Returns the zero maxtrix
pub fn zero() -> Self {
ProjectionMatrix([[0.0; 4]; 4])
}
/// Returns the matrix which shift the coordinate
pub fn shift(x: f64, y: f64, z: f64) -> Self {
ProjectionMatrix([
[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],
])
}
/// Returns the matrix which rotates the coordinate
pub fn rotate(x: f64, y: f64, z: f64) -> Self {
let (c, b, a) = (x, y, z);
ProjectionMatrix([
[
a.cos() * b.cos(),
a.cos() * b.sin() * c.sin() - a.sin() * c.cos(),
a.cos() * b.sin() * c.cos() + a.sin() * c.sin(),
0.0,
],
[
a.sin() * b.cos(),
a.sin() * b.sin() * c.sin() + a.cos() * c.cos(),
a.sin() * b.sin() * c.cos() - a.cos() * c.sin(),
0.0,
],
[-b.sin(), b.cos() * c.sin(), b.cos() * c.cos(), 0.0],
[0.0, 0.0, 0.0, 1.0],
])
}
/// Returns the matrix that applies a scale factor
pub fn scale(factor: f64) -> Self {
ProjectionMatrix([
[1.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 1.0 / factor],
])
}
/// Normalize the matrix, this will make the metric unit to 1
pub fn normalize(&mut self) {
if self.0[3][3] > 1e-20 {
for r in 0..4 {
for c in 0..4 {
self.0[r][c] /= self.0[3][3];
}
}
}
}
/// Get the distance of the point in guest coordinate from the screen in pixels
pub fn projected_depth(&self, (x, y, z): (i32, i32, i32)) -> i32 {
let r = &self.0[2];
(r[0] * x as f64 + r[1] * y as f64 + r[2] * z as f64 + r[3]) as i32
}
}
/// The helper struct to build a projection matrix
#[derive(Copy, Clone)]
pub struct ProjectionMatrixBuilder {
pub yaw: f64,
pub pitch: f64,
pub scale: f64,
pivot_before: (i32, i32, i32),
pivot_after: (i32, i32),
}
impl ProjectionMatrixBuilder {
pub fn new() -> Self {
Self {
yaw: 0.5,
pitch: 0.15,
scale: 1.0,
pivot_after: (0, 0),
pivot_before: (0, 0, 0),
}
}
/// Set the pivot point, which means the 3D coordinate "before" should be mapped into
/// the 2D coordinatet "after"
pub fn set_pivot(&mut self, before: (i32, i32, i32), after: (i32, i32)) -> &mut Self {
self.pivot_before = before;
self.pivot_after = after;
self
}
/// Build the matrix based on the configuration
pub fn into_matrix(self) -> ProjectionMatrix {
let mut ret = if self.pivot_before == (0, 0, 0) {
ProjectionMatrix::default()
} else {
let (x, y, z) = self.pivot_before;
ProjectionMatrix::shift(-x as f64, -y as f64, -z as f64) * ProjectionMatrix::default()
};
if self.yaw.abs() > 1e-20 {
ret = ret * ProjectionMatrix::rotate(0.0, self.yaw, 0.0);
}
if self.pitch.abs() > 1e-20 {
ret = ret * ProjectionMatrix::rotate(self.pitch, 0.0, 0.0);
}
if (self.scale - 1.0).abs() > 1e-20 {
ret = ret * ProjectionMatrix::scale(self.scale);
}
if self.pivot_after != (0, 0) {
let (x, y) = self.pivot_after;
ret = ret * ProjectionMatrix::shift(x as f64, y as f64, 0.0);
}
ret
}
}
|
