scad_tree_math/

mt4.rs

// MIT License
//
// Copyright (c) 2023 Michael H. Phillips
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//

use crate::{dcos, dsin, dtan, Pt3, Pt4};

/// A matrix with column major order.
#[derive(Clone, Copy, Default, PartialEq)]
pub struct Mt4 {
    pub x: Pt4,
    pub y: Pt4,
    pub z: Pt4,
    pub w: Pt4,
}

impl std::fmt::Display for Mt4 {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        writeln!(f, "| {} {} {} {} |", self.x.x, self.y.x, self.z.x, self.w.x)?;
        writeln!(f, "| {} {} {} {} |", self.x.y, self.y.y, self.z.y, self.w.y)?;
        writeln!(f, "| {} {} {} {} |", self.x.z, self.y.z, self.z.z, self.w.z)?;
        writeln!(f, "| {} {} {} {} |", self.x.w, self.y.w, self.z.w, self.w.w)
    }
}

impl Mt4 {
    pub fn new(x: Pt4, y: Pt4, z: Pt4, w: Pt4) -> Self {
        Self { x, y, z, w }
    }

    pub fn transposed(&self) -> Self {
        Mt4::new(
            Pt4::new(self.x.x, self.y.x, self.z.x, self.w.x),
            Pt4::new(self.x.y, self.y.y, self.z.y, self.w.y),
            Pt4::new(self.x.z, self.y.z, self.z.z, self.w.z),
            Pt4::new(self.x.w, self.y.w, self.z.w, self.w.w),
        )
    }

    pub fn identity() -> Self {
        Mt4::new(
            Pt4::new(1.0, 0.0, 0.0, 0.0),
            Pt4::new(0.0, 1.0, 0.0, 0.0),
            Pt4::new(0.0, 0.0, 1.0, 0.0),
            Pt4::new(0.0, 0.0, 0.0, 1.0),
        )
    }

    pub fn scale_matrix(x: f64, y: f64, z: f64) -> Self {
        let mut result = Mt4::identity();
        result.x.x = x;
        result.y.y = y;
        result.z.z = z;
        result
    }

    pub fn translate_matrix(x: f64, y: f64, z: f64) -> Self {
        let mut result = Mt4::identity();
        result.w.x = x;
        result.w.y = y;
        result.w.z = z;
        result
    }

    pub fn rot_x_matrix(degrees: f64) -> Self {
        let c = dcos(degrees);
        let s = dsin(degrees);
        Mt4::new(
            Pt4::new(1.0, 0.0, 0.0, 0.0),
            Pt4::new(0.0, c, -s, 0.0),
            Pt4::new(0.0, s, c, 0.0),
            Pt4::new(0.0, 0.0, 0.0, 1.0),
        )
        .transposed()
    }

    pub fn rot_y_matrix(degrees: f64) -> Self {
        let c = dcos(degrees);
        let s = dsin(degrees);
        Mt4::new(
            Pt4::new(c, 0.0, s, 0.0),
            Pt4::new(0.0, 1.0, 0.0, 0.0),
            Pt4::new(-s, 0.0, c, 0.0),
            Pt4::new(0.0, 0.0, 0.0, 1.0),
        )
        .transposed()
    }

    pub fn rot_z_matrix(degrees: f64) -> Self {
        let c = dcos(degrees);
        let s = dsin(degrees);
        Mt4::new(
            Pt4::new(c, -s, 0.0, 0.0),
            Pt4::new(s, c, 0.0, 0.0),
            Pt4::new(0.0, 0.0, 1.0, 0.0),
            Pt4::new(0.0, 0.0, 0.0, 1.0),
        )
        .transposed()
    }

    pub fn rot_vec(x: f64, y: f64, z: f64, degrees: f64) -> Self {
        let c = dcos(degrees);
        let s = dsin(degrees);
        Mt4::new(
            Pt4::new(
                c + x * x * (1.0 - c),
                x * y * (1.0 - c) - z * s,
                x * z * (1.0 - c) + y * s,
                0.0,
            ),
            Pt4::new(
                y * x * (1.0 - c) + z * s,
                c + y * y * (1.0 - c),
                y * z * (1.0 - c) - x * s,
                0.0,
            ),
            Pt4::new(
                z * x * (1.0 - c) - z * s,
                z * y * (1.0 - c) + x * s,
                c + z * z * (1.0 - c),
                0.0,
            ),
            Pt4::new(0.0, 0.0, 0.0, 1.0),
        )
        .transposed()
    }

    pub fn perspective_matrix(fovy: f64, aspect: f64, near: f64, far: f64) -> Self {
        let tan_half_fovy = dtan(fovy / 2.0);
        Mt4::new(
            Pt4::new(1.0 / (aspect * tan_half_fovy), 0.0, 0.0, 0.0),
            Pt4::new(0.0, 1.0 / tan_half_fovy, 0.0, 0.0),
            Pt4::new(
                0.0,
                0.0,
                -(far + near) / (far - near),
                -(2.0 * far * near) / (far - near),
            ),
            Pt4::new(0.0, 0.0, -1.0, 1.0),
        )
        .transposed()
    }

    pub fn inverse(&self) -> Option<Self> {
        let mut out = Mt4::identity();

        out[0] = self[5] * self[10] * self[15]
            - self[5] * self[11] * self[14]
            - self[9] * self[6] * self[15]
            + self[9] * self[7] * self[14]
            + self[13] * self[6] * self[11]
            - self[13] * self[7] * self[10];

        out[4] = -self[4] * self[10] * self[15]
            + self[4] * self[11] * self[14]
            + self[8] * self[6] * self[15]
            - self[8] * self[7] * self[14]
            - self[12] * self[6] * self[11]
            + self[12] * self[7] * self[10];

        out[8] = self[4] * self[9] * self[15]
            - self[4] * self[11] * self[13]
            - self[8] * self[5] * self[15]
            + self[8] * self[7] * self[13]
            + self[12] * self[5] * self[11]
            - self[12] * self[7] * self[9];

        out[12] = -self[4] * self[9] * self[14]
            + self[4] * self[10] * self[13]
            + self[8] * self[5] * self[14]
            - self[8] * self[6] * self[13]
            - self[12] * self[5] * self[10]
            + self[12] * self[6] * self[9];

        out[1] = -self[1] * self[10] * self[15]
            + self[1] * self[11] * self[14]
            + self[9] * self[2] * self[15]
            - self[9] * self[3] * self[14]
            - self[13] * self[2] * self[11]
            + self[13] * self[3] * self[10];

        out[5] = self[0] * self[10] * self[15]
            - self[0] * self[11] * self[14]
            - self[8] * self[2] * self[15]
            + self[8] * self[3] * self[14]
            + self[12] * self[2] * self[11]
            - self[12] * self[3] * self[10];

        out[9] = -self[0] * self[9] * self[15]
            + self[0] * self[11] * self[13]
            + self[8] * self[1] * self[15]
            - self[8] * self[3] * self[13]
            - self[12] * self[1] * self[11]
            + self[12] * self[3] * self[9];

        out[13] = self[0] * self[9] * self[14]
            - self[0] * self[10] * self[13]
            - self[8] * self[1] * self[14]
            + self[8] * self[2] * self[13]
            + self[12] * self[1] * self[10]
            - self[12] * self[2] * self[9];

        out[2] = self[1] * self[6] * self[15]
            - self[1] * self[7] * self[14]
            - self[5] * self[2] * self[15]
            + self[5] * self[3] * self[14]
            + self[13] * self[2] * self[7]
            - self[13] * self[3] * self[6];

        out[6] = -self[0] * self[6] * self[15]
            + self[0] * self[7] * self[14]
            + self[4] * self[2] * self[15]
            - self[4] * self[3] * self[14]
            - self[12] * self[2] * self[7]
            + self[12] * self[3] * self[6];

        out[10] = self[0] * self[5] * self[15]
            - self[0] * self[7] * self[13]
            - self[4] * self[1] * self[15]
            + self[4] * self[3] * self[13]
            + self[12] * self[1] * self[7]
            - self[12] * self[3] * self[5];

        out[14] = -self[0] * self[5] * self[14]
            + self[0] * self[6] * self[13]
            + self[4] * self[1] * self[14]
            - self[4] * self[2] * self[13]
            - self[12] * self[1] * self[6]
            + self[12] * self[2] * self[5];

        out[3] = -self[1] * self[6] * self[11]
            + self[1] * self[7] * self[10]
            + self[5] * self[2] * self[11]
            - self[5] * self[3] * self[10]
            - self[9] * self[2] * self[7]
            + self[9] * self[3] * self[6];

        out[7] = self[0] * self[6] * self[11]
            - self[0] * self[7] * self[10]
            - self[4] * self[2] * self[11]
            + self[4] * self[3] * self[10]
            + self[8] * self[2] * self[7]
            - self[8] * self[3] * self[6];

        out[11] = -self[0] * self[5] * self[11]
            + self[0] * self[7] * self[9]
            + self[4] * self[1] * self[11]
            - self[4] * self[3] * self[9]
            - self[8] * self[1] * self[7]
            + self[8] * self[3] * self[5];

        out[15] = self[0] * self[5] * self[10]
            - self[0] * self[6] * self[9]
            - self[4] * self[1] * self[10]
            + self[4] * self[2] * self[9]
            + self[8] * self[1] * self[6]
            - self[8] * self[2] * self[5];

        let mut det = self[0] * out[0] + self[1] * out[4] + self[2] * out[8] + self[3] * out[12];

        if det == 0.0 {
            None
        } else {
            det = 1.0 / det;
            for i in 0..16 {
                out[i] = out[i] * det;
            }
            Some(out)
        }
    }

    pub fn look_at_matrix_rh(eye: Pt3, center: Pt3, up: Pt3) -> Self {
        let mut f = center - eye;
        f = f.normalized();
        let mut s = f.cross(up);
        s = s.normalized();
        let u = s.cross(f);
        Mt4::new(
            Pt4::new(s.x, s.y, s.z, -s.dot(eye)),
            Pt4::new(u.x, u.y, u.z, -u.dot(eye)),
            Pt4::new(-f.x, -f.y, -f.z, f.dot(eye)),
            Pt4::new(0.0, 0.0, 0.0, 1.0),
        )
    }

    pub fn look_at_matrix_lh(eye: Pt3, center: Pt3, up: Pt3) -> Self {
        let mut f = center - eye;
        f = f.normalized();
        let mut s = up.cross(f);
        // parallel check
        if s == Pt3::new(0.0, 0.0, 0.0) {
            // anti-parallel check
            if up.dot(f) < 0.0 {
                return Mt4::rot_x_matrix(180.0);
            }
            return Mt4::identity();
        }
        s = s.normalized();
        let u = f.cross(s);
        Mt4::new(
            Pt4::new(s.x, s.y, s.z, -s.dot(eye)),
            Pt4::new(u.x, u.y, u.z, -u.dot(eye)),
            Pt4::new(f.x, f.y, f.z, -f.dot(eye)),
            Pt4::new(0.0, 0.0, 0.0, 1.0),
        )
    }

    pub fn rotation_from_direction(direction: Pt3, up: Pt3) -> Self {
        let x_axis: Pt3 = up.cross(direction).normalized();
        let z_axis: Pt3 = direction.cross(x_axis).normalized();
        let mut result = Mt4::identity();
        result.x.x = x_axis.x;
        result.x.y = direction.x;
        result.x.z = z_axis.x;

        result.y.x = x_axis.y;
        result.y.y = direction.y;
        result.y.z = z_axis.y;

        result.z.x = x_axis.z;
        result.z.y = direction.z;
        result.z.z = z_axis.z;

        result
    }
}

impl std::ops::Mul<Pt4> for Mt4 {
    type Output = Pt4;

    fn mul(self, rhs: Pt4) -> Self::Output {
        let t = self.transposed();
        Pt4::new(t.x.dot(rhs), t.y.dot(rhs), t.z.dot(rhs), t.w.dot(rhs))
    }
}

impl std::ops::Mul<Pt3> for Mt4 {
    type Output = Pt3;

    fn mul(self, rhs: Pt3) -> Self::Output {
        let t = self.transposed();
        Pt3::new(
            t.x.as_pt3().dot(rhs),
            t.y.as_pt3().dot(rhs),
            t.z.as_pt3().dot(rhs),
        )
    }
}

impl std::ops::Mul<Mt4> for Mt4 {
    type Output = Mt4;

    fn mul(self, rhs: Mt4) -> Self::Output {
        let t = self.transposed();
        Mt4::new(
            Pt4::new(
                t.x.dot(rhs.x),
                t.y.dot(rhs.x),
                t.z.dot(rhs.x),
                t.w.dot(rhs.x),
            ),
            Pt4::new(
                t.x.dot(rhs.y),
                t.y.dot(rhs.y),
                t.z.dot(rhs.y),
                t.w.dot(rhs.y),
            ),
            Pt4::new(
                t.x.dot(rhs.z),
                t.y.dot(rhs.z),
                t.z.dot(rhs.z),
                t.w.dot(rhs.z),
            ),
            Pt4::new(
                t.x.dot(rhs.w),
                t.y.dot(rhs.w),
                t.z.dot(rhs.w),
                t.w.dot(rhs.w),
            ),
        )
    }
}

impl std::ops::Index<usize> for Mt4 {
    type Output = f64;

    fn index(&self, index: usize) -> &Self::Output {
        match index {
            0 => &self.x.x,
            1 => &self.x.y,
            2 => &self.x.z,
            3 => &self.x.w,
            4 => &self.y.x,
            5 => &self.y.y,
            6 => &self.y.z,
            7 => &self.y.w,
            8 => &self.z.x,
            9 => &self.z.y,
            10 => &self.z.z,
            11 => &self.z.w,
            12 => &self.w.x,
            13 => &self.w.y,
            14 => &self.w.z,
            15 => &self.w.w,
            _ => panic!("Index out of bounds"),
        }
    }
}

impl std::ops::IndexMut<usize> for Mt4 {
    fn index_mut(&mut self, index: usize) -> &mut Self::Output {
        match index {
            0 => &mut self.x.x,
            1 => &mut self.x.y,
            2 => &mut self.x.z,
            3 => &mut self.x.w,
            4 => &mut self.y.x,
            5 => &mut self.y.y,
            6 => &mut self.y.z,
            7 => &mut self.y.w,
            8 => &mut self.z.x,
            9 => &mut self.z.y,
            10 => &mut self.z.z,
            11 => &mut self.z.w,
            12 => &mut self.w.x,
            13 => &mut self.w.y,
            14 => &mut self.w.z,
            15 => &mut self.w.w,
            _ => panic!("Index out of bounds"),
        }
    }
}