bgc-c/basic-geometry/quaternion.c

#include "quaternion.h"

// =============== Normalization ================ //

int bg_fp32_quaternion_normalize(BgFP32Quaternion* quaternion)
{
    const float square_modulus = bg_fp32_quaternion_get_square_modulus(quaternion);

    if (1.0f - BG_FP32_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + BG_FP32_TWO_EPSYLON) {
        return 1;
    }

    if (square_modulus <= BG_FP32_SQUARE_EPSYLON) {
        bg_fp32_quaternion_reset(quaternion);
        return 0;
    }

    const float multiplier = sqrtf(1.0f / square_modulus);

    quaternion->s0 *= multiplier;
    quaternion->x1 *= multiplier;
    quaternion->x2 *= multiplier;
    quaternion->x3 *= multiplier;

    return 1;
}

int bg_fp64_quaternion_normalize(BgFP64Quaternion* quaternion)
{
    const double square_modulus = bg_fp64_quaternion_get_square_modulus(quaternion);

    if (1.0 - BG_FP64_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0 + BG_FP64_TWO_EPSYLON) {
        return 1;
    }

    if (square_modulus <= BG_FP32_SQUARE_EPSYLON) {
        bg_fp64_quaternion_reset(quaternion);
        return 0;
    }

    const double multiplier = sqrt(1.0 / square_modulus);

    quaternion->s0 *= multiplier;
    quaternion->x1 *= multiplier;
    quaternion->x2 *= multiplier;
    quaternion->x3 *= multiplier;

    return 1;
}

// ============ Make Rotation Matrix ============ //

void bg_fp32_quaternion_get_rotation_matrix(const BgFP32Quaternion* quaternion, BgFP32Matrix3x3* matrix)
{
    const float s0s0 = quaternion->s0 * quaternion->s0;
    const float x1x1 = quaternion->x1 * quaternion->x1;
    const float x2x2 = quaternion->x2 * quaternion->x2;
    const float x3x3 = quaternion->x3 * quaternion->x3;

    const float square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);

    if (-BG_FP32_EPSYLON <= square_modulus && square_modulus <= BG_FP32_EPSYLON)
    {
        bg_fp32_matrix3x3_set_to_identity(matrix);
        return;
    }

    const float corrector1 = 1.0f / square_modulus;
    const float corrector2 = 2.0f * corrector1;

    const float s0x1 = quaternion->s0 * quaternion->x1;
    const float s0x2 = quaternion->s0 * quaternion->x2;
    const float s0x3 = quaternion->s0 * quaternion->x3;
    const float x1x2 = quaternion->x1 * quaternion->x2;
    const float x1x3 = quaternion->x1 * quaternion->x3;
    const float x2x3 = quaternion->x2 * quaternion->x3;

    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    matrix->r1c2 = corrector2 * (x1x2 - s0x3);
    matrix->r2c3 = corrector2 * (x2x3 - s0x1);
    matrix->r3c1 = corrector2 * (x1x3 - s0x2);

    matrix->r2c1 = corrector2 * (x1x2 + s0x3);
    matrix->r3c2 = corrector2 * (x2x3 + s0x1);
    matrix->r1c3 = corrector2 * (x1x3 + s0x2);
}

void bg_fp64_quaternion_get_rotation_matrix(const BgFP64Quaternion* quaternion, BgFP64Matrix3x3* matrix)
{
    const double s0s0 = quaternion->s0 * quaternion->s0;
    const double x1x1 = quaternion->x1 * quaternion->x1;
    const double x2x2 = quaternion->x2 * quaternion->x2;
    const double x3x3 = quaternion->x3 * quaternion->x3;

    const double square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);

    if (-BG_FP64_EPSYLON <= square_modulus && square_modulus <= BG_FP64_EPSYLON)
    {
        bg_fp64_matrix3x3_set_to_identity(matrix);
        return;
    }

    const double corrector1 = 1.0f / square_modulus;
    const double corrector2 = 2.0f * corrector1;

    const double s0x1 = quaternion->s0 * quaternion->x1;
    const double s0x2 = quaternion->s0 * quaternion->x2;
    const double s0x3 = quaternion->s0 * quaternion->x3;
    const double x1x2 = quaternion->x1 * quaternion->x2;
    const double x1x3 = quaternion->x1 * quaternion->x3;
    const double x2x3 = quaternion->x2 * quaternion->x3;

    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    matrix->r1c2 = corrector2 * (x1x2 - s0x3);
    matrix->r2c3 = corrector2 * (x2x3 - s0x1);
    matrix->r3c1 = corrector2 * (x1x3 - s0x2);

    matrix->r2c1 = corrector2 * (x1x2 + s0x3);
    matrix->r3c2 = corrector2 * (x2x3 + s0x1);
    matrix->r1c3 = corrector2 * (x1x3 + s0x2);
}

// ============ Make Reverse Matrix ============= //

void bg_fp32_quaternion_get_reverse_matrix(const BgFP32Quaternion* quaternion, BgFP32Matrix3x3* matrix)
{
    const float s0s0 = quaternion->s0 * quaternion->s0;
    const float x1x1 = quaternion->x1 * quaternion->x1;
    const float x2x2 = quaternion->x2 * quaternion->x2;
    const float x3x3 = quaternion->x3 * quaternion->x3;

    const float square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);

    if (-BG_FP32_EPSYLON <= square_modulus && square_modulus <= BG_FP32_EPSYLON)
    {
        bg_fp32_matrix3x3_set_to_identity(matrix);
        return;
    }

    const float corrector1 = 1.0f / square_modulus;
    const float corrector2 = 2.0f * corrector1;

    const float s0x1 = quaternion->s0 * quaternion->x1;
    const float s0x2 = quaternion->s0 * quaternion->x2;
    const float s0x3 = quaternion->s0 * quaternion->x3;
    const float x1x2 = quaternion->x1 * quaternion->x2;
    const float x1x3 = quaternion->x1 * quaternion->x3;
    const float x2x3 = quaternion->x2 * quaternion->x3;

    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    matrix->r1c2 = corrector2 * (x1x2 + s0x3);
    matrix->r2c3 = corrector2 * (x2x3 + s0x1);
    matrix->r3c1 = corrector2 * (x1x3 + s0x2);

    matrix->r2c1 = corrector2 * (x1x2 - s0x3);
    matrix->r3c2 = corrector2 * (x2x3 - s0x1);
    matrix->r1c3 = corrector2 * (x1x3 - s0x2);
}

void bg_fp64_quaternion_get_reverse_matrix(const BgFP64Quaternion* quaternion, BgFP64Matrix3x3* matrix)
{
    const double s0s0 = quaternion->s0 * quaternion->s0;
    const double x1x1 = quaternion->x1 * quaternion->x1;
    const double x2x2 = quaternion->x2 * quaternion->x2;
    const double x3x3 = quaternion->x3 * quaternion->x3;

    const double square_modulus = (s0s0 + x1x1) + (x2x2 + x3x3);

    if (-BG_FP64_EPSYLON <= square_modulus && square_modulus <= BG_FP64_EPSYLON)
    {
        bg_fp64_matrix3x3_set_to_identity(matrix);
        return;
    }

    const double corrector1 = 1.0f / square_modulus;
    const double corrector2 = 2.0f * corrector1;

    const double s0x1 = quaternion->s0 * quaternion->x1;
    const double s0x2 = quaternion->s0 * quaternion->x2;
    const double s0x3 = quaternion->s0 * quaternion->x3;
    const double x1x2 = quaternion->x1 * quaternion->x2;
    const double x1x3 = quaternion->x1 * quaternion->x3;
    const double x2x3 = quaternion->x2 * quaternion->x3;

    matrix->r1c1 = corrector1 * ((s0s0 + x1x1) - (x2x2 + x3x3));
    matrix->r2c2 = corrector1 * ((s0s0 + x2x2) - (x1x1 + x3x3));
    matrix->r3c3 = corrector1 * ((s0s0 + x3x3) - (x1x1 + x2x2));

    matrix->r1c2 = corrector2 * (x1x2 + s0x3);
    matrix->r2c3 = corrector2 * (x2x3 + s0x1);
    matrix->r3c1 = corrector2 * (x1x3 + s0x2);

    matrix->r2c1 = corrector2 * (x1x2 - s0x3);
    matrix->r3c2 = corrector2 * (x2x3 - s0x1);
    matrix->r1c3 = corrector2 * (x1x3 - s0x2);
}

// ================== Product =================== //

void bg_fp32_quaternion_get_product(const BgFP32Quaternion* left, const BgFP32Quaternion* right, BgFP32Quaternion* product)
{
    const float s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
    const float x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
    const float x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
    const float x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);

    product->s0 = s0;
    product->x1 = x1;
    product->x2 = x2;
    product->x3 = x3;
}

void bg_fp64_quaternion_get_product(const BgFP64Quaternion* left, const BgFP64Quaternion* right, BgFP64Quaternion* product)
{
    const double s0 = (left->s0 * right->s0 - left->x1 * right->x1) - (left->x2 * right->x2 + left->x3 * right->x3);
    const double x1 = (left->x1 * right->s0 + left->s0 * right->x1) - (left->x3 * right->x2 - left->x2 * right->x3);
    const double x2 = (left->x2 * right->s0 + left->s0 * right->x2) - (left->x1 * right->x3 - left->x3 * right->x1);
    const double x3 = (left->x3 * right->s0 + left->s0 * right->x3) - (left->x2 * right->x1 - left->x1 * right->x2);

    product->s0 = s0;
    product->x1 = x1;
    product->x2 = x2;
    product->x3 = x3;
}