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Expose mat4 determinant and add test. Consolidate common calculations. #40

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Jan 14, 2024
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Expose mat4 determinant and add test. Consolidate common calculations. #40

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10dc416
Expose mat4 determinant and add test. Consolidate common calculations.
Nairou Jan 12, 2024
c21c3b8
const fixes for newer compiler
Nairou Jan 12, 2024
8c3f392
Clean up signs for readability
Nairou Jan 12, 2024
f6385d5
Zig fmt didn't like the extra spaces
Nairou Jan 13, 2024
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114 changes: 60 additions & 54 deletions src/mat4.zig
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Original file line number Diff line number Diff line change
Expand Up @@ -340,66 +340,59 @@ pub fn Mat4x4(comptime T: type) type {
return result;
}

fn detsubs(self: Self) [12]T {
return .{
self.data[0][0] * self.data[1][1] - self.data[1][0] * self.data[0][1],
self.data[0][0] * self.data[1][2] - self.data[1][0] * self.data[0][2],
self.data[0][0] * self.data[1][3] - self.data[1][0] * self.data[0][3],
self.data[0][1] * self.data[1][2] - self.data[1][1] * self.data[0][2],
self.data[0][1] * self.data[1][3] - self.data[1][1] * self.data[0][3],
self.data[0][2] * self.data[1][3] - self.data[1][2] * self.data[0][3],

self.data[2][0] * self.data[3][1] - self.data[3][0] * self.data[2][1],
self.data[2][0] * self.data[3][2] - self.data[3][0] * self.data[2][2],
self.data[2][0] * self.data[3][3] - self.data[3][0] * self.data[2][3],
self.data[2][1] * self.data[3][2] - self.data[3][1] * self.data[2][2],
self.data[2][1] * self.data[3][3] - self.data[3][1] * self.data[2][3],
self.data[2][2] * self.data[3][3] - self.data[3][2] * self.data[2][3],
};
}

/// Calculate determinant of the given 4x4 matrix.
pub fn det(self: Self) T {
const s = detsubs(self);
return s[0] * s[11] - s[1] * s[10] + s[2] * s[9] + s[3] * s[8] - s[4] * s[7] + s[5] * s[6];
}

/// Construct inverse 4x4 from given matrix.
/// Note: This is not the most efficient way to do this.
/// TODO: Make it more efficient.
pub fn inv(self: Self) Self {
var inv_mat: Self = undefined;

var s: [6]T = undefined;
var c: [6]T = undefined;

s[0] = self.data[0][0] * self.data[1][1] - self.data[1][0] * self.data[0][1];
s[1] = self.data[0][0] * self.data[1][2] - self.data[1][0] * self.data[0][2];
s[2] = self.data[0][0] * self.data[1][3] - self.data[1][0] * self.data[0][3];
s[3] = self.data[0][1] * self.data[1][2] - self.data[1][1] * self.data[0][2];
s[4] = self.data[0][1] * self.data[1][3] - self.data[1][1] * self.data[0][3];
s[5] = self.data[0][2] * self.data[1][3] - self.data[1][2] * self.data[0][3];

c[0] = self.data[2][0] * self.data[3][1] - self.data[3][0] * self.data[2][1];
c[1] = self.data[2][0] * self.data[3][2] - self.data[3][0] * self.data[2][2];
c[2] = self.data[2][0] * self.data[3][3] - self.data[3][0] * self.data[2][3];
c[3] = self.data[2][1] * self.data[3][2] - self.data[3][1] * self.data[2][2];
c[4] = self.data[2][1] * self.data[3][3] - self.data[3][1] * self.data[2][3];
c[5] = self.data[2][2] * self.data[3][3] - self.data[3][2] * self.data[2][3];

const determ = 1 / (s[0] * c[5] - s[1] * c[4] + s[2] * c[3] + s[3] * c[2] - s[4] * c[1] + s[5] * c[0]);

inv_mat.data[0][0] =
(self.data[1][1] * c[5] - self.data[1][2] * c[4] + self.data[1][3] * c[3]) * determ;
inv_mat.data[0][1] =
(-self.data[0][1] * c[5] + self.data[0][2] * c[4] - self.data[0][3] * c[3]) * determ;
inv_mat.data[0][2] =
(self.data[3][1] * s[5] - self.data[3][2] * s[4] + self.data[3][3] * s[3]) * determ;
inv_mat.data[0][3] =
(-self.data[2][1] * s[5] + self.data[2][2] * s[4] - self.data[2][3] * s[3]) * determ;

inv_mat.data[1][0] =
(-self.data[1][0] * c[5] + self.data[1][2] * c[2] - self.data[1][3] * c[1]) * determ;
inv_mat.data[1][1] =
(self.data[0][0] * c[5] - self.data[0][2] * c[2] + self.data[0][3] * c[1]) * determ;
inv_mat.data[1][2] =
(-self.data[3][0] * s[5] + self.data[3][2] * s[2] - self.data[3][3] * s[1]) * determ;
inv_mat.data[1][3] =
(self.data[2][0] * s[5] - self.data[2][2] * s[2] + self.data[2][3] * s[1]) * determ;

inv_mat.data[2][0] =
(self.data[1][0] * c[4] - self.data[1][1] * c[2] + self.data[1][3] * c[0]) * determ;
inv_mat.data[2][1] =
(-self.data[0][0] * c[4] + self.data[0][1] * c[2] - self.data[0][3] * c[0]) * determ;
inv_mat.data[2][2] =
(self.data[3][0] * s[4] - self.data[3][1] * s[2] + self.data[3][3] * s[0]) * determ;
inv_mat.data[2][3] =
(-self.data[2][0] * s[4] + self.data[2][1] * s[2] - self.data[2][3] * s[0]) * determ;

inv_mat.data[3][0] =
(-self.data[1][0] * c[3] + self.data[1][1] * c[1] - self.data[1][2] * c[0]) * determ;
inv_mat.data[3][1] =
(self.data[0][0] * c[3] - self.data[0][1] * c[1] + self.data[0][2] * c[0]) * determ;
inv_mat.data[3][2] =
(-self.data[3][0] * s[3] + self.data[3][1] * s[1] - self.data[3][2] * s[0]) * determ;
inv_mat.data[3][3] =
(self.data[2][0] * s[3] - self.data[2][1] * s[1] + self.data[2][2] * s[0]) * determ;
const s = detsubs(self);

const determ = 1 / (s[0] * s[11] - s[1] * s[10] + s[2] * s[9] + s[3] * s[8] - s[4] * s[7] + s[5] * s[6]);

inv_mat.data[0][0] = determ * (self.data[1][1] * s[11] - self.data[1][2] * s[10] + self.data[1][3] * s[9]);
inv_mat.data[0][1] = determ * -(self.data[0][1] * s[11] - self.data[0][2] * s[10] + self.data[0][3] * s[9]);
inv_mat.data[0][2] = determ * (self.data[3][1] * s[5] - self.data[3][2] * s[4] + self.data[3][3] * s[3]);
inv_mat.data[0][3] = determ * -(self.data[2][1] * s[5] - self.data[2][2] * s[4] + self.data[2][3] * s[3]);

inv_mat.data[1][0] = determ * -(self.data[1][0] * s[11] - self.data[1][2] * s[8] + self.data[1][3] * s[7]);
inv_mat.data[1][1] = determ * (self.data[0][0] * s[11] - self.data[0][2] * s[8] + self.data[0][3] * s[7]);
inv_mat.data[1][2] = determ * -(self.data[3][0] * s[5] - self.data[3][2] * s[2] + self.data[3][3] * s[1]);
inv_mat.data[1][3] = determ * (self.data[2][0] * s[5] - self.data[2][2] * s[2] + self.data[2][3] * s[1]);

inv_mat.data[2][0] = determ * (self.data[1][0] * s[10] - self.data[1][1] * s[8] + self.data[1][3] * s[6]);
inv_mat.data[2][1] = determ * -(self.data[0][0] * s[10] - self.data[0][1] * s[8] + self.data[0][3] * s[6]);
inv_mat.data[2][2] = determ * (self.data[3][0] * s[4] - self.data[3][1] * s[2] + self.data[3][3] * s[0]);
inv_mat.data[2][3] = determ * -(self.data[2][0] * s[4] - self.data[2][1] * s[2] + self.data[2][3] * s[0]);

inv_mat.data[3][0] = determ * -(self.data[1][0] * s[9] - self.data[1][1] * s[7] + self.data[1][2] * s[6]);
inv_mat.data[3][1] = determ * (self.data[0][0] * s[9] - self.data[0][1] * s[7] + self.data[0][2] * s[6]);
inv_mat.data[3][2] = determ * -(self.data[3][0] * s[3] - self.data[3][1] * s[1] + self.data[3][2] * s[0]);
inv_mat.data[3][3] = determ * (self.data[2][0] * s[3] - self.data[2][1] * s[1] + self.data[2][2] * s[0]);

return inv_mat;
}
Expand Down Expand Up @@ -615,6 +608,19 @@ test "zalgebra.Mat4.scale" {
});
}

test "zalgebra.Mat4.det" {
const a: Mat4 = .{
.data = .{
.{ 2, 0, 0, 4 },
.{ 0, 2, 0, 0 },
.{ 0, 0, 2, 0 },
.{ 4, 0, 0, 2 },
},
};

try expectEqual(a.det(), -48);
}

test "zalgebra.Mat4.inv" {
const a: Mat4 = .{
.data = .{
Expand Down
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