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Diffstat (limited to 'maths.cpp')
| -rw-r--r-- | maths.cpp | 296 |
1 files changed, 296 insertions, 0 deletions
diff --git a/maths.cpp b/maths.cpp new file mode 100644 index 0000000..ed8948f --- /dev/null +++ b/maths.cpp @@ -0,0 +1,296 @@ +#include "maths.hpp" + +m4f::m4f() {} + +m4f::m4f(float d) { + for (int y = 0; y < 4; y++) { + for (int x = 0; x < 4; x++) { + m[x][y] = 0.0f; + } + } + + m[0][0] = d; + m[1][1] = d; + m[2][2] = d; + m[3][3] = d; +} + +m4f m4f::identity() { + return m4f(1.0f); +} + +m4f m4f::screenspace(float hw, float hh) { + m4f r(1.0f); + + r.m[0][0] = hw; + r.m[0][3] = hw; + r.m[1][1] = -hh; + r.m[1][3] = hh; + + return r; +} + +m4f m4f::operator*(const m4f& other) const { + m4f r(1.0f); + + r.m[0][0] = m[0][0] * other.m[0][0] + m[1][0] * other.m[0][1] + m[2][0] * other.m[0][2] + m[3][0] * other.m[0][3]; + r.m[1][0] = m[0][0] * other.m[1][0] + m[1][0] * other.m[1][1] + m[2][0] * other.m[1][2] + m[3][0] * other.m[1][3]; + r.m[2][0] = m[0][0] * other.m[2][0] + m[1][0] * other.m[2][1] + m[2][0] * other.m[2][2] + m[3][0] * other.m[2][3]; + r.m[3][0] = m[0][0] * other.m[3][0] + m[1][0] * other.m[3][1] + m[2][0] * other.m[3][2] + m[3][0] * other.m[3][3]; + r.m[0][1] = m[0][1] * other.m[0][0] + m[1][1] * other.m[0][1] + m[2][1] * other.m[0][2] + m[3][1] * other.m[0][3]; + r.m[1][1] = m[0][1] * other.m[1][0] + m[1][1] * other.m[1][1] + m[2][1] * other.m[1][2] + m[3][1] * other.m[1][3]; + r.m[2][1] = m[0][1] * other.m[2][0] + m[1][1] * other.m[2][1] + m[2][1] * other.m[2][2] + m[3][1] * other.m[2][3]; + r.m[3][1] = m[0][1] * other.m[3][0] + m[1][1] * other.m[3][1] + m[2][1] * other.m[3][2] + m[3][1] * other.m[3][3]; + r.m[0][2] = m[0][2] * other.m[0][0] + m[1][2] * other.m[0][1] + m[2][2] * other.m[0][2] + m[3][2] * other.m[0][3]; + r.m[1][2] = m[0][2] * other.m[1][0] + m[1][2] * other.m[1][1] + m[2][2] * other.m[1][2] + m[3][2] * other.m[1][3]; + r.m[2][2] = m[0][2] * other.m[2][0] + m[1][2] * other.m[2][1] + m[2][2] * other.m[2][2] + m[3][2] * other.m[2][3]; + r.m[3][2] = m[0][2] * other.m[3][0] + m[1][2] * other.m[3][1] + m[2][2] * other.m[3][2] + m[3][2] * other.m[3][3]; + r.m[0][3] = m[0][3] * other.m[0][0] + m[1][3] * other.m[0][1] + m[2][3] * other.m[0][2] + m[3][3] * other.m[0][3]; + r.m[1][3] = m[0][3] * other.m[1][0] + m[1][3] * other.m[1][1] + m[2][3] * other.m[1][2] + m[3][3] * other.m[1][3]; + r.m[2][3] = m[0][3] * other.m[2][0] + m[1][3] * other.m[2][1] + m[2][3] * other.m[2][2] + m[3][3] * other.m[2][3]; + r.m[3][3] = m[0][3] * other.m[3][0] + m[1][3] * other.m[3][1] + m[2][3] * other.m[3][2] + m[3][3] * other.m[3][3]; + + return r; +} + +v4f m4f::operator*(const v4f& other) const { + return v4f( + m[0][0] * other.x + m[1][0] * other.y + m[2][0] * other.z + m[3][0] + other.w, + m[0][1] * other.x + m[1][1] * other.y + m[2][1] * other.z + m[3][1] + other.w, + m[0][2] * other.x + m[1][2] * other.y + m[2][2] * other.z + m[3][2] + other.w, + m[0][3] * other.x + m[1][3] * other.y + m[2][3] * other.z + m[3][3] + other.w); +} + +m4f m4f::translate(m4f m, v3f v) { + m4f r(1.0f); + + r.m[3][0] += v.x; + r.m[3][1] += v.y; + r.m[3][2] += v.z; + + return m * r; +} + +m4f m4f::rotate(m4f m, float a, v3f v) { + m4f r(1.0f); + + const float c = cosf(a); + const float s = sinf(a); + + const float omc = (float)1 - c; + + const float x = v.x; + const float y = v.y; + const float z = v.z; + + r.m[0][0] = x * x * omc + c; + r.m[0][1] = y * x * omc + z * s; + r.m[0][2] = x * z * omc - y * s; + r.m[1][0] = x * y * omc - z * s; + r.m[1][1] = y * y * omc + c; + r.m[1][2] = y * z * omc + x * s; + r.m[2][0] = x * z * omc + y * s; + r.m[2][1] = y * z * omc - x * s; + r.m[2][2] = z * z * omc + c; + + return m * r; +} + +m4f m4f::scale(m4f m, v3f v) { + m4f r(1.0f); + + r.m[0][0] = v.x; + r.m[1][1] = v.y; + r.m[2][2] = v.z; + + return m * r; +} + + +v3f m4f::get_translation() { + return v3f(m[3][0], m[3][1], m[3][2]); +} + +m4f m4f::lookat(v3f c, v3f o, v3f u) { + m4f r(1.0f); + + const v3f f = v3f::normalised(o - c); + u = v3f::normalised(u); + const v3f s = v3f::normalised(v3f::cross(f, u)); + u = v3f::cross(s, f); + + r.m[0][0] = s.x; + r.m[1][0] = s.y; + r.m[2][0] = s.z; + r.m[0][1] = u.x; + r.m[1][1] = u.y; + r.m[2][1] = u.z; + r.m[0][2] = -f.x; + r.m[1][2] = -f.y; + r.m[2][2] = -f.z; + r.m[3][0] = -v3f::dot(s, c); + r.m[3][1] = -v3f::dot(u, c); + r.m[3][2] = v3f::dot(f, c); + + return r; +} + +m4f m4f::pers(float fov, float asp, float n, float f) { + m4f r(0.0f); + + float fov_rad = to_rad(fov); + float focal_length = 1.0f / tanf(fov_rad / 2.0f); + + float x = focal_length / asp; + float y = -focal_length; + float a = f / (n - f); + float b = n * a; + + r.m[0][0] = x; + r.m[1][1] = y; + r.m[2][2] = a; + r.m[3][2] = b; + r.m[2][3] = -1.0f; + + return r; +} + +m4f m4f::orth(float l, float r, float b, float t, float n, float f) { + m4f res(1.0f); + + float* data = (float*)res.m; + + float lr = 1.0f / (l - r); + float bt = 1.0f / (b - t); + float nf = 1.0f / (n - f); + + data[0] = -2.0f * lr; + data[5] = -2.0f * bt; + data[10] = 2.0f * nf; + + data[12] = (l + r) * lr; + data[13] = (t + b) * bt; + data[14] = (f + n) * nf; + + return res; +} + +m4f m4f::inverse() { + const float* mm = (float*)m; + + float t0 = mm[10] * mm[15]; + float t1 = mm[14] * mm[11]; + float t2 = mm[6] * mm[15]; + float t3 = mm[14] * mm[7]; + float t4 = mm[6] * mm[11]; + float t5 = mm[10] * mm[7]; + float t6 = mm[2] * mm[15]; + float t7 = mm[14] * mm[3]; + float t8 = mm[2] * mm[11]; + float t9 = mm[10] * mm[3]; + float t10 = mm[2] * mm[7]; + float t11 = mm[6] * mm[3]; + float t12 = mm[8] * mm[13]; + float t13 = mm[12] * mm[9]; + float t14 = mm[4] * mm[13]; + float t15 = mm[12] * mm[5]; + float t16 = mm[4] * mm[9]; + float t17 = mm[8] * mm[5]; + float t18 = mm[0] * mm[13]; + float t19 = mm[12] * mm[1]; + float t20 = mm[0] * mm[9]; + float t21 = mm[8] * mm[1]; + float t22 = mm[0] * mm[5]; + float t23 = mm[4] * mm[1]; + + m4f r(1.0f); + float* o = (float*)r.m; + + o[0] = (t0 * mm[5] + t3 * mm[9] + t4 * mm[13]) - (t1 * mm[5] + t2 * mm[9] + t5 * mm[13]); + o[1] = (t1 * mm[1] + t6 * mm[9] + t9 * mm[13]) - (t0 * mm[1] + t7 * mm[9] + t8 * mm[13]); + o[2] = (t2 * mm[1] + t7 * mm[5] + t10 * mm[13]) - (t3 * mm[1] + t6 * mm[5] + t11 * mm[13]); + o[3] = (t5 * mm[1] + t8 * mm[5] + t11 * mm[9]) - (t4 * mm[1] + t9 * mm[5] + t10 * mm[9]); + + float d = 1.0f / (mm[0] * o[0] + mm[4] * o[1] + mm[8] * o[2] + mm[12] * o[3]); + + o[0] = d * o[0]; + o[1] = d * o[1]; + o[2] = d * o[2]; + o[3] = d * o[3]; + o[4] = d * ((t1 * mm[4] + t2 * mm[8] + t5 * mm[12]) - (t0 * mm[4] + t3 * mm[8] + t4 * mm[12])); + o[5] = d * ((t0 * mm[0] + t7 * mm[8] + t8 * mm[12]) - (t1 * mm[0] + t6 * mm[8] + t9 * mm[12])); + o[6] = d * ((t3 * mm[0] + t6 * mm[4] + t11 * mm[12]) - (t2 * mm[0] + t7 * mm[4] + t10 * mm[12])); + o[7] = d * ((t4 * mm[0] + t9 * mm[4] + t10 * mm[8]) - (t5 * mm[0] + t8 * mm[4] + t11 * mm[8])); + o[8] = d * ((t12 * mm[7] + t15 * mm[11] + t16 * mm[15]) - (t13 * mm[7] + t14 * mm[11] + t17 * mm[15])); + o[9] = d * ((t13 * mm[3] + t18 * mm[11] + t21 * mm[15]) - (t12 * mm[3] + t19 * mm[11] + t20 * mm[15])); + o[10] = d * ((t14 * mm[3] + t19 * mm[7] + t22 * mm[15]) - (t15 * mm[3] + t18 * mm[7] + t23 * mm[15])); + o[11] = d * ((t17 * mm[3] + t20 * mm[7] + t23 * mm[11]) - (t16 * mm[3] + t21 * mm[7] + t22 * mm[11])); + o[12] = d * ((t14 * mm[10] + t17 * mm[14] + t13 * mm[6]) - (t16 * mm[14] + t12 * mm[6] + t15 * mm[10])); + o[13] = d * ((t20 * mm[14] + t12 * mm[2] + t19 * mm[10]) - (t18 * mm[10] + t21 * mm[14] + t13 * mm[2])); + o[14] = d * ((t18 * mm[6] + t23 * mm[14] + t15 * mm[2]) - (t22 * mm[14] + t14 * mm[2] + t19 * mm[6])); + o[15] = d * ((t22 * mm[10] + t16 * mm[2] + t21 * mm[6]) - (t20 * mm[6] + t23 * mm[10] + t17 * mm[2])); + + return r; +} + +m4f m4f::transposed() { + m4f r(1.0f); + + r.m[0][0] = m[0][0]; + r.m[1][0] = m[0][1]; + r.m[2][0] = m[0][2]; + r.m[3][0] = m[0][3]; + r.m[0][1] = m[1][0]; + r.m[1][1] = m[1][1]; + r.m[2][1] = m[1][2]; + r.m[3][1] = m[1][3]; + r.m[0][2] = m[2][0]; + r.m[1][2] = m[2][1]; + r.m[2][2] = m[2][2]; + r.m[3][2] = m[2][3]; + r.m[0][3] = m[3][0]; + r.m[1][3] = m[3][1]; + r.m[2][3] = m[3][2]; + r.m[3][3] = m[3][3]; + + return r; +} + +v4f m4f::transform(m4f m, v4f v) { + return v4f( + m.m[0][0] * v.x + m.m[1][0] * v.y + m.m[2][0] * v.z + m.m[3][0] + v.w, + m.m[0][1] * v.x + m.m[1][1] * v.y + m.m[2][1] * v.z + m.m[3][1] + v.w, + m.m[0][2] * v.x + m.m[1][2] * v.y + m.m[2][2] * v.z + m.m[3][2] + v.w, + m.m[0][3] * v.x + m.m[1][3] * v.y + m.m[2][3] * v.z + m.m[3][3] + v.w); +} + +AABB m4f::transform(m4f m, AABB aabb) { + v3f corners[] = { + aabb.min, + v3f(aabb.min.x, aabb.max.y, aabb.min.z), + v3f(aabb.min.x, aabb.max.y, aabb.max.z), + v3f(aabb.min.x, aabb.min.y, aabb.max.z), + v3f(aabb.max.x, aabb.min.y, aabb.min.z), + v3f(aabb.max.x, aabb.max.y, aabb.min.z), + aabb.max, + v3f(aabb.max.x, aabb.min.y, aabb.max.z) + }; + + AABB result = { + .min = { INFINITY, INFINITY, INFINITY }, + .max = { -INFINITY, -INFINITY, -INFINITY } + }; + + for (int i = 0; i < 8; i++) { + v4f point = m4f::transform(m, v4f(corners[i].x, corners[i].y, corners[i].z, 0.0f)); + + result.min.x = std::min(result.min.x, point.x); + result.min.y = std::min(result.min.y, point.y); + result.min.z = std::min(result.min.z, point.z); + result.max.x = std::max(result.max.x, point.x); + result.max.y = std::max(result.max.y, point.y); + result.max.z = std::max(result.max.z, point.z); + } + + return result; +} |