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@@ -3,394 +3,6 @@ package linalg
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import "core:math"
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import "core:math"
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import "intrinsics"
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import "intrinsics"
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-// Generic
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-
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-@private IS_NUMERIC :: intrinsics.type_is_numeric;
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-@private IS_QUATERNION :: intrinsics.type_is_quaternion;
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-@private IS_ARRAY :: intrinsics.type_is_array;
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-
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-
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-vector_dot :: proc(a, b: $T/[$N]$E) -> (c: E) where IS_NUMERIC(E) {
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- for i in 0..<N {
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- c += a[i] * b[i];
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- }
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- return;
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-}
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-quaternion128_dot :: proc(a, b: $T/quaternion128) -> (c: f32) {
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- return real(a)*real(a) + imag(a)*imag(b) + jmag(a)*jmag(b) + kmag(a)*kmag(b);
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-}
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-quaternion256_dot :: proc(a, b: $T/quaternion256) -> (c: f64) {
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- return real(a)*real(a) + imag(a)*imag(b) + jmag(a)*jmag(b) + kmag(a)*kmag(b);
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-}
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-
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-dot :: proc{vector_dot, quaternion128_dot, quaternion256_dot};
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-
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-quaternion_inverse :: proc(q: $Q) -> Q where IS_QUATERNION(Q) {
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- return conj(q) * quaternion(1.0/dot(q, q), 0, 0, 0);
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-}
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-
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-
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-vector_cross2 :: proc(a, b: $T/[2]$E) -> E where IS_NUMERIC(E) {
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- return a[0]*b[1] - b[0]*a[1];
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-}
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-
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-vector_cross3 :: proc(a, b: $T/[3]$E) -> (c: T) where IS_NUMERIC(E) {
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- c[0] = a[1]*b[2] - b[1]*a[2];
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- c[1] = a[2]*b[0] - b[2]*a[0];
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- c[2] = a[0]*b[1] - b[0]*a[1];
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- return;
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-}
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-
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-vector_cross :: proc{vector_cross2, vector_cross3};
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-cross :: vector_cross;
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-
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-vector_normalize :: proc(v: $T/[$N]$E) -> T where IS_NUMERIC(E) {
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- return v / length(v);
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-}
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-quaternion_normalize :: proc(q: $Q) -> Q where IS_QUATERNION(Q) {
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- return q/abs(q);
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-}
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-normalize :: proc{vector_normalize, quaternion_normalize};
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-
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-vector_normalize0 :: proc(v: $T/[$N]$E) -> T where IS_NUMERIC(E) {
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- m := length(v);
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- return m == 0 ? 0 : v/m;
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-}
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-quaternion_normalize0 :: proc(q: $Q) -> Q where IS_QUATERNION(Q) {
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- m := abs(q);
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- return m == 0 ? 0 : q/m;
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-}
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-normalize0 :: proc{vector_normalize0, quaternion_normalize0};
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-
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-
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-vector_length :: proc(v: $T/[$N]$E) -> E where IS_NUMERIC(E) {
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- return math.sqrt(dot(v, v));
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-}
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-
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-vector_length2 :: proc(v: $T/[$N]$E) -> E where IS_NUMERIC(E) {
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- return dot(v, v);
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-}
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-
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-quaternion_length :: proc(q: $Q) -> Q where IS_QUATERNION(Q) {
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- return abs(q);
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-}
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-
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-quaternion_length2 :: proc(q: $Q) -> Q where IS_QUATERNION(Q) {
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- return dot(q, q);
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-}
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-
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-length :: proc{vector_length, quaternion_length};
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-length2 :: proc{vector_length2, quaternion_length2};
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-
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-
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-vector_lerp :: proc(x, y, t: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- ti := t[i];
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- s[i] = x[i]*(1-ti) + y[i]*ti;
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- }
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- return s;
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-}
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-
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-vector_unlerp :: proc(a, b, x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- ai := a[i];
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- s[i] = (x[i]-ai)/(b[i]-ai);
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- }
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- return s;
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-}
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-
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-vector_sin :: proc(angle: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.sin(angle[i]);
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- }
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- return s;
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-}
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-
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-vector_cos :: proc(angle: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.cos(angle[i]);
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- }
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- return s;
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-}
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-
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-vector_tan :: proc(angle: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.tan(angle[i]);
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- }
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- return s;
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-}
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-
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-
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-vector_asin :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.asin(x[i]);
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- }
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- return s;
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-}
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-
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-vector_acos :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.acos(x[i]);
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- }
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- return s;
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-}
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-
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-vector_atan :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.atan(x[i]);
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- }
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- return s;
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-}
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-
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-vector_atan2 :: proc(y, x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.atan(y[i], x[i]);
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- }
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- return s;
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-}
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-
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-vector_pow :: proc(x, y: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.pow(x[i], y[i]);
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- }
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- return s;
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-}
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-
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-vector_expr :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.expr(x[i]);
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- }
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- return s;
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-}
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-
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-vector_sqrt :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.sqrt(x[i]);
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- }
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- return s;
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-}
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-
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-vector_abs :: proc(x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = abs(x[i]);
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- }
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- return s;
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-}
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-
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-vector_sign :: proc(v: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.sign(v[i]);
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- }
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- return s;
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-}
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-
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-vector_floor :: proc(v: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.floor(v[i]);
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- }
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- return s;
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-}
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-
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-vector_ceil :: proc(v: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.ceil(v[i]);
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- }
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- return s;
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-}
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-
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-
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-vector_mod :: proc(x, y: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = math.mod(x[i], y[i]);
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- }
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- return s;
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-}
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-
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-vector_min :: proc(a, b: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = min(a[i], b[i]);
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- }
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- return s;
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-}
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-
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-vector_max :: proc(a, b: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = max(a[i], b[i]);
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- }
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- return s;
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-}
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-
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-vector_clamp :: proc(x, a, b: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = clamp(x[i], a[i], b[i]);
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- }
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- return s;
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-}
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-
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-vector_mix :: proc(x, y, a: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = x[i]*(1-a[i]) + y[i]*a[i];
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- }
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- return s;
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-}
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-
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-vector_step :: proc(edge, x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- s[i] = x[i] < edge[i] ? 0 : 1;
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- }
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- return s;
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-}
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-
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-vector_smoothstep :: proc(edge0, edge1, x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- e0, e1 := edge0[i], edge1[i];
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- t := clamp((x[i] - e0) / (e1 - e0), 0, 1);
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- s[i] = t * t * (3 - 2*t);
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- }
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- return s;
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-}
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-
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-vector_smootherstep :: proc(edge0, edge1, x: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- s: V;
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- for i in 0..<N {
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- e0, e1 := edge0[i], edge1[i];
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- t := clamp((x[i] - e0) / (e1 - e0), 0, 1);
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- s[i] = t * t * t * (t * (6*t - 15) + 10);
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- }
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- return s;
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-}
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-
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-vector_distance :: proc(p0, p1: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- return length(p1 - p0);
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-}
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-
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-vector_reflect :: proc(i, n: $V/[$N]$E) -> V where IS_NUMERIC(E) {
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- b := n * (2 * dot(n, i));
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- return i - b;
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-}
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-
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-vector_refract :: proc(i, n: $V/[$N]$E, eta: E) -> V where IS_NUMERIC(E) {
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- dv := dot(n, i);
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- k := 1 - eta*eta - (1 - dv*dv);
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- a := i * eta;
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- b := n * eta*dv*math.sqrt(k);
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- return (a - b) * E(int(k >= 0));
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-}
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-
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-
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-
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-identity :: proc($T: typeid/[$N][N]$E) -> (m: T) {
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- for i in 0..<N do m[i][i] = E(1);
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- return m;
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-}
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-
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-transpose :: proc(a: $T/[$N][$M]$E) -> (m: T) {
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- for j in 0..<M {
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- for i in 0..<N {
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- m[j][i] = a[i][j];
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- }
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- }
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- return;
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-}
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-
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-matrix_mul :: proc(a, b: $M/[$N][N]$E) -> (c: M)
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- where !IS_ARRAY(E),
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- IS_NUMERIC(E) {
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- for i in 0..<N {
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- for k in 0..<N {
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- for j in 0..<N {
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- c[k][i] += a[j][i] * b[k][j];
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- }
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- }
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- }
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- return;
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-}
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-
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-matrix_mul_differ :: proc(a: $A/[$J][$I]$E, b: $B/[$K][J]E) -> (c: [K][I]E)
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- where !IS_ARRAY(E),
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- IS_NUMERIC(E),
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- I != K {
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- for k in 0..<K {
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- for j in 0..<J {
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- for i in 0..<I {
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- c[k][i] += a[j][i] * b[k][j];
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- }
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- }
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- }
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- return;
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-}
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-
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-
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-matrix_mul_vector :: proc(a: $A/[$I][$J]$E, b: $B/[I]E) -> (c: B)
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- where !IS_ARRAY(E),
|
|
|
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- IS_NUMERIC(E) {
|
|
|
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- for i in 0..<I {
|
|
|
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- for j in 0..<J {
|
|
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- c[i] += a[i][j] * b[i];
|
|
|
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- }
|
|
|
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- }
|
|
|
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- return;
|
|
|
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-}
|
|
|
|
-
|
|
|
|
-quaternion128_mul_vector3 :: proc(q: $Q/quaternion128, v: $V/[3]$F/f32) -> V {
|
|
|
|
- Raw_Quaternion :: struct {xyz: [3]f32, r: f32};
|
|
|
|
-
|
|
|
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- q := transmute(Raw_Quaternion)q;
|
|
|
|
- v := transmute([3]f32)v;
|
|
|
|
-
|
|
|
|
- t := cross(2*q.xyz, v);
|
|
|
|
- return V(v + q.r*t + cross(q.xyz, t));
|
|
|
|
-}
|
|
|
|
-
|
|
|
|
-quaternion256_mul_vector3 :: proc(q: $Q/quaternion256, v: $V/[3]$F/f64) -> V {
|
|
|
|
- Raw_Quaternion :: struct {xyz: [3]f64, r: f64};
|
|
|
|
-
|
|
|
|
- q := transmute(Raw_Quaternion)q;
|
|
|
|
- v := transmute([3]f64)v;
|
|
|
|
-
|
|
|
|
- t := cross(2*q.xyz, v);
|
|
|
|
- return V(v + q.r*t + cross(q.xyz, t));
|
|
|
|
-}
|
|
|
|
-quaternion_mul_vector3 :: proc{quaternion128_mul_vector3, quaternion256_mul_vector3};
|
|
|
|
-
|
|
|
|
-mul :: proc{
|
|
|
|
- matrix_mul,
|
|
|
|
- matrix_mul_differ,
|
|
|
|
- matrix_mul_vector,
|
|
|
|
- quaternion128_mul_vector3,
|
|
|
|
- quaternion256_mul_vector3,
|
|
|
|
-};
|
|
|
|
-
|
|
|
|
-vector_to_ptr :: proc(v: ^$V/[$N]$E) -> ^E where IS_NUMERIC(E) {
|
|
|
|
- return &v[0];
|
|
|
|
-}
|
|
|
|
-matrix_to_ptr :: proc(m: ^$A/[$I][$J]$E) -> ^E where IS_NUMERIC(E) {
|
|
|
|
- return &m[0][0];
|
|
|
|
-}
|
|
|
|
-
|
|
|
|
|
|
|
|
// Specific
|
|
// Specific
|
|
|
|
|