bgc-c/basic-geometry/versor.c

#include <math.h>

#include "angle.h"
#include "versor.h"

const BgFP32Versor BG_FP32_IDLE_VERSOR = { 1.0f, 0.0f, 0.0f, 0.0f };

const BgFP64Versor BG_FP64_IDLE_VERSOR = { 1.0, 0.0, 0.0, 0.0 };

void __bg_fp32_versor_normalize(const float square_module, __BgFP32DarkTwinVersor* twin)
{
    if (square_module <= BG_FP32_SQUARE_EPSYLON || (twin->s0 * twin->s0) >= (1.0f - BG_FP32_TWO_EPSYLON) * square_module) {
        twin->s0 = 1.0f;
        twin->x1 = 0.0f;
        twin->x2 = 0.0f;
        twin->x3 = 0.0f;
        return;
    }

    const float module = sqrtf(square_module);

    twin->s0 /= module;
    twin->x1 /= module;
    twin->x2 /= module;
    twin->x3 /= module;
}

void __bg_fp64_versor_normalize(const double square_module, __BgFP64DarkTwinVersor* twin)
{
    if (square_module <= BG_FP64_SQUARE_EPSYLON || (twin->s0 * twin->s0) >= (1.0 - BG_FP64_TWO_EPSYLON) * square_module) {
        twin->s0 = 1.0;
        twin->x1 = 0.0;
        twin->x2 = 0.0;
        twin->x3 = 0.0;
        return;
    }

    const double module = sqrt(square_module);

    twin->s0 /= module;
    twin->x1 /= module;
    twin->x2 /= module;
    twin->x3 /= module;
}

// =============== Set Crude Turn =============== //

void bg_fp32_versor_set_crude_turn(const float x1, const float x2, const float x3, const float angle, const angle_unit_t unit, BgFP32Versor* result)
{
    const float square_vector = x1 * x1 + x2 * x2 + x3 * x3;

    if (square_vector <= BG_FP32_SQUARE_EPSYLON) {
        bg_fp32_versor_reset(result);
        return;
    }

    const float half_angle = bg_fp32_angle_to_radians(0.5f * angle, unit);

    const float sine = sinf(half_angle);

    if (-BG_FP32_EPSYLON <= sine && sine <= BG_FP32_EPSYLON) {
        bg_fp32_versor_reset(result);
        return;
    }

    const float multiplier = sine / sqrtf(square_vector);

    bg_fp32_versor_set_values(cosf(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier, result);
}

void bg_fp64_versor_set_crude_turn(const double x1, const double x2, const double x3, const double angle, const angle_unit_t unit, BgFP64Versor* result)
{
    const double square_vector = x1 * x1 + x2 * x2 + x3 * x3;

    if (square_vector <= BG_FP64_SQUARE_EPSYLON) {
        bg_fp64_versor_reset(result);
        return;
    }

    const double half_angle = bg_fp64_angle_to_radians(0.5 * angle, unit);

    const double sine = sin(half_angle);

    if (-BG_FP64_EPSYLON <= sine && sine <= BG_FP64_EPSYLON) {
        bg_fp64_versor_reset(result);
        return;
    }

    const double multiplier = sine / sqrt(square_vector);

    bg_fp64_versor_set_values(cos(half_angle), x1 * multiplier, x2 * multiplier, x3 * multiplier, result);
}

// ================= Rotation3 ================== //

void bg_fp32_versor_get_rotation(const BgFP32Versor* versor, BgFP32Rotation3* result)
{
    if (versor == 0 || result == 0) {
        return;
    }

    if (versor->s0 <= -(1.0f - BG_FP32_EPSYLON) || 1.0f - BG_FP32_EPSYLON <= versor->s0) {
        bg_fp32_rotation_reset(result);
        return;
    }

    const float square_vector = versor->x1 * versor->x1 + versor->x2 * versor->x2 + versor->x3 * versor->x3;

    result->radians = 2.0f * acosf(versor->s0 / sqrtf(versor->s0 * versor->s0 + square_vector));

    const float vector_module = sqrtf(square_vector);

    result->axis.x1 = versor->x1 / vector_module;
    result->axis.x2 = versor->x2 / vector_module;
    result->axis.x3 = versor->x3 / vector_module;
}

void bg_fp64_versor_get_rotation(const BgFP64Versor* versor, BgFP64Rotation3* result)
{
    if (versor == 0 || result == 0) {
        return;
    }

    if (versor->s0 <= -(1.0 - BG_FP64_EPSYLON) || 1.0 - BG_FP64_EPSYLON <= versor->s0) {
        bg_fp64_rotation_reset(result);
        return;
    }

    const double square_vector = versor->x1 * versor->x1 + versor->x2 * versor->x2 + versor->x3 * versor->x3;

    result->radians = 2.0 * acos(versor->s0 / sqrt(versor->s0 * versor->s0 + square_vector));

    const double vector_module = sqrt(square_vector);

    result->axis.x1 = versor->x1 / vector_module;
    result->axis.x2 = versor->x2 / vector_module;
    result->axis.x3 = versor->x3 / vector_module;
}